Methods and kits for guided stem cell differentiation

ABSTRACT

The present disclosure provides methods, and related kits, for directing cell attachment and spreading on a substrate and inducing isotropic spreading of cells; provides methods, and related kits, for cell sorting; and further provides methods, and related kits, for guided induction of stem cell differentiation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to co-pending U.S. patent application Ser.No. ______, filed Jul. 18, 2017, entitled, “Methods and kits for cellsorting,” and co-pending U.S. patent application Ser. No. ______, filedJul. 18, 2017, entitled, “Methods and kits for directing cell attachmentand spreading,” both of which are incorporated herein by reference intheir entireties.

GOVERNMENT SUPPORT

The subject invention was made with government support under a researchproject supported by the National Science Foundation (NSF) CAREERprogram grant number 0845954. The government has certain rights in theinvention.

BACKGROUND

The interactions between cells and their surrounding environments havebeen receiving increased attention over the past twenty years.Cell-substrate interactions can profoundly affect cell behavior,including adhesion, spreading, migration, division, differentiation,apoptosis, and internal cellular signaling. The binding interactionsbetween cells and their material layer(s) are influenced by mechanicalstimuli, such as material stiffness and material curvatures. The effectsof material stiffness on cell behaviors have been extensively studied(Alenghat and Ingber, 2002; Wang et al., 2002; Janmey and Weitz, 2004;Yeung et al., 2004; Engler et al., 2004; Chen et al., 2004; Wong et al.,2004; Brown et al., 2006; Engler et al., 2006; Kasza et al., 2007;Rodriguez et al., 2013); however, the cellular responses to the geometryof a substrate, e.g., the curvature of the substrate, are notwell-documented (Chen et al., 1997; Sniadecki et al., 2006; Sanz-Herreraet al., 2009; Digabel et al., 2010; Baker and Chen, 2012). Since thematerials on which the cells grow in vivo are normally not flat, theresponses of cells to material curvatures should also be a fundamentalaspect of cell mechanosensitivity and mechanotransduction. Theimportance of material curvature effects on cell behaviors can beillustrated by understanding the process of cell attachment and growthon curved surfaces of bones and implants in vivo.

Normal cell natural spreading is random in every direction, and theresulting cell spread shape is irregular and non-uniform (Alberts etal., 2015). Two-dimensional (2D) geometric patterns and chemicalpatterns have been widely generated by microfabrication technologies todefine the spread shapes of living cells in in vitro cultures, which hasopened many opportunities for and re-shaped the area of cellularbioengineering and mechanobiology (Kilian et al, 2010; Wan et al., 2010;Tang et al., 2012; Tao et al., 2013). Cell isotropic-spreading, wherethe resulting cell outline or boundary is roughly circular and smoothwhich means the extent of the cell spreading in every direction isroughly the same from the geometric center of the cell, has beenrealized by culturing the cells in geometrically-patterned andchemically-patterned circular areas (Chen et al., 1997; Liu and Chen,2007; Song et al., 2011), but the geometric patterning and or thechemical patterning must be there to control or restrict the spreadingof a cell to realize the cell isotropic-spreading, which means therealized cell isotropic-spreading is not a cell natural spreading.Therefore, it is difficult to take advantage of or use cellisotropic-spreading realized by culturing cells ingeometrically-patterned and chemically-patterned circular areas forstudies and applications in cellular bioengineering and mechano-biology.

Further, in response to geometrical stimuli cells change theirmorphologies and motilities, and these changes are most likely caused bythe changes in the intracellular forces associated with the changes inthe cell focal adhesions and actin stress fibers due to the geometricalstimuli (Folch and Toner, 2000; Discher et al., 2005; Georges andJanmey, 2005; Vogel and Sheetz, 2006; Vartanian et al., 2008; Cheng etal., 2009; Wan et al., 2010; Rape et al., 2011; Song et al., 2011; Yaoet al., 2013; Meehan and Nain, 2014). The geometry of a substrate alsodetermines the orientation and rate of cell growth (Smeal et al., 2005;Rumpler et al., 2008; Hwang et al., 2009; Veiseh et al., 2015;Viswanathan et al., 2015; Zadpoor, 2015).

BRIEF SUMMARY

Since the surface curvature of a substrate is a major descriptiveparameter of the geometry of the substrate, studies on the cellularresponses to the surface curvature of a substrate are necessary forunderstanding the cellular behaviors in three-dimensional (3-D)micromechanical environments and for designing effective and efficient3-D micromechanical environments to control cell and tissuedevelopments. It is difficult to take advantage of or use cellisotropic-spreading realized by culturing cells ingeometrically-patterned and chemically-patterned circular areas forstudies and applications in cellular bioengineering and mechanobiology.Methods to control spreading of a cell on a non-flat substrate areneeded, especially, for 3-D bioengineering and mechanobiology.

The present disclosure provides methods, and related kits, for directingcell attachment and spreading on a substrate and inducing isotropicspreading of cells. The disclosure also provides methods, and relatedkits, for cell sorting; and further provides methods, and related kits,for guided induction of stem cell differentiation.

In one aspect, the disclosure provides methods of cell sorting,comprising culturing a mixed population of cell types, the mixedpopulation comprising a target cell and a non-target cell, on a curvedsubstrate in the presence of cell culture media for a time sufficientfor one of a target or a non-target cell to attach to the substrate; andremoving, or separating, the cell culture media from the curvedsubstrate, wherein the target cell is contained either in the cellculture media or on the curved substrate, wherein the non-target cell iscontained in the cell culture media if the target cell is contained onthe curved substrate or the non-target cell is contained on the curvedsubstrate if the target cell is contained in the cell culture media. Ina further aspect, the disclosure provides kits for cell sorting,comprising a first reagent, wherein the first reagent comprises a curvedsubstrate. In yet another aspect, the disclosure provides kits for cellsorting, comprising a first reagent, wherein the first reagent comprisesa spherical substrate having a diameter less than about 500 μm.

In another aspect, the present disclosure provides methods for directingcell attachment and spreading on a substrate, comprising culturing acell on a curved substrate in the presence of cell culture media,wherein attachment and spreading increases as the curvature of thesubstrate decreases. In a further aspect, the disclosure provides kitsfor directing cell attachment and spreading on a substrate, comprising afirst reagent, wherein the first reagent comprises a curved substrate.

In another aspect, the disclosure provides methods for guided inductionof stem cell differentiation, comprising culturing a stem cell on acurved substrate in the presence of cell culture media. In a furtheraspect, the disclosure provides kits for guided induction of stem celldifferentiation, comprising a first reagent, wherein the first reagentcomprises a curved substrate.

In one aspect, the present disclosure provides methods of culturingcells on micro ball embedded polyacrylamide (PA) gels (non-flat and 3-D)such that the cells isotropically spread over the balls and the adjacentgel surfaces. In another aspect, the disclosure provides methods ofinducing isotropic spreading of cells, comprising culturing a cell on acurved substrate, the curved substrate partially embedded in a gelsurface, wherein the cell isotropically spreads over the curvedsubstrate and onto the gel surface. In a further aspect, the disclosureprovides kits for inducing isotropic spreading of cells, comprising afirst reagent, wherein the first reagent comprises a curved substrate.

In some embodiments, the curved substrate comprises an array of curvedsubstrates.

The methods, and related kits, herein described can be used inconnection with pharmaceutical, medical, and veterinary applications, aswell as fundamental scientific research and methodologies, as would beidentifiable by a skilled person upon reading of the present disclosure.These and other objects, features and advantages of the presentdisclosure will become clearer when the drawings, as well as thedetailed description, are taken into consideration.

BRIEF DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the nature of the present disclosure,reference should be had to the following detailed description taken inconnection with the accompanying figures.

FIGS. 1, 2, 3 and 4 illustrate various embodiments of microstructuresembedded in various material layers.

FIG. 5 illustrates an array of various clusters of microstructures.

FIG. 6 illustrates differentiation responses of human adipose-derivedmesenchymal stem cells (hMSCs) with various differentiation media.

FIG. 7 illustrates gene expression experiments by real-time polymerasechain reaction (RT-PCR or qPCR)

FIG. 8 shows a graph of adipogenesis induced by substrate curvatures.Relative gene expression (PPARG) is graphed relative to ball diameter.

FIG. 9 shows a graph of osteogenesis induced by substrate curvatures andosteocyte differentiation induction media. Relative gene expression(RUNX2) is graphed relative to ball diameter.

FIG. 10 shows a frontal sectional view of a schematic illustration ofthe different configurations of a cell wrapping over a micro glass ballembedded on the surface of a polyacrylamide (PA) gel.

FIG. 11 shows a phase-contrast image of NIH-3T3 fibroblasts growing on amicro glass ball embedded PA gel with a Young's modulus of 75 kPa after48 hours in culture. The left blue arrow in A (image was taken by usinga 10× objective) indicates a slightly spread cell on the gel surface,and the right red arrow in A points to a cell wrapped over a micro glassball and an enlarged view of this cell is shown in B (image was taken byusing a 40× objective).

FIG. 12 shows a phase-contrast image of NIH-3T3 fibroblasts growing on amicro glass ball embedded PA gel with a Young's modulus of 10 kPa after96 hours in culture. The red arrow in A (image was taken by using a 10×objective) points to two cells wrapped over two micro glass balls and anenlarged view of these two cells is shown in B (image was taken by usinga 40× objective).

FIG. 13 shows phase-contrast images of NIH-3T3 fibroblasts growing onmicro glass ball embedded PA gels with a Young's modulus of 1 kPa. Theimage shown in A was taken after 48 hours in culture. The red arrow in A(image was taken by using a 10× objective) points to a cell wrapped overa micro glass ball and an enlarged view of this cell is shown in B(image was taken by using a 40× objective). The image shown in C wastaken after 96 hours in culture. The red arrow in C (image was taken byusing a 10× objective) points to two cells wrapped over a micro glassball and an enlarged view of these two cells is shown in D (image wastaken by using a 40× objective).

FIG. 14 shows a three-dimensional (3-D) schematic drawing to show thespeculated mechanism or process to form the observed cell naturalisotropic-spreading here, i.e., the speculated process for a cell towrap over a micro glass ball.

FIG. 15 shows micro glass ball embedded PA gel experimental platformsproviding unique and powerful 3-D micromechanical environments to studycell mechanobiological responses to substrate curvatures and localsubstrate stiffness. (a) Schematic drawing of a platform. (b)-(c)Bright-field optical pictures of two experimental platforms withembedded glass balls having diameters of 500 μm and 2 mm, respectively.

FIG. 16 shows effects of substrate curvatures on the spreadingmorphologies of the NIH-3T3 fibroblasts. As is known, the surfacecurvature of a substrate is the reciprocal of the radius of thesubstrate. The fibroblasts were plated on the PA gels embedded withmicro glass balls having diameters from 5 μm to 2 mm, and thephase-contrast images were taken after 24 hours in culture. Fibroblastsgrowing on a flat glass plate (22 mm-square glass coverslip) (a), and ona 2 mm-(b), 1.1 mm-(c), 900 μm-(d), 750 μm-(e), 500 μm-(f), 147 μm-(g),and 58 μm-(h) diameter glass ball are indicated by the white arrows.Scale bars (except the one in the inset of (h)): 100 μm.

FIG. 17 shows cell length and width versus ball diameter for the NIH-3T3fibroblasts. The cell lengths and widths were measured for a number ofrandomly-selected cells (n_(fibroblasts)=95) growing on the flat glassplates and on the glass balls. For the fibroblasts growing on the flatglass plates, 10 cells were measured, and for the fibroblasts growing onthe 2 mm-, 1.1 mm-, 900 μm-, 750 μm-, and 500 μm-diameter glass balls,10 cells were measured for each ball diameter, and the results shown aremean±standard deviation (SD) for each ball diameter including the caseof the flat glass plates. For the fibroblasts growing on the glass ballswith diameters of 300 μm and below, since the cell attachment rates ofthese balls were much lower than those of the balls with diameters of500 μm and above, 35 cells in total were measured, and the results shownare for each individual cell.

FIG. 18 shows cell spread area versus ball diameter for the NIH-3T3fibroblasts measured in FIG. 17. In contrast to FIG. 17, here, for thefibroblasts growing on the glass balls with diameters of 500 μm andabove, besides the mean±SD result for each ball diameter, the spreadarea of each individual fibroblast is also shown. *: p<0.05; **: p<0.01;***: p<0.001.

FIG. 19 shows effects of the substrate curvatures on the spreadingmorphologies of the normal human adipose-derived mesenchymal stem cells(hMSCs). The hMSCs were plated on the PA gels embedded with micro glassballs having diameters from 5 μm to 4 mm, and the phase-contrast imageswere taken after 96 h in culture (since the hMSCs spread much slowerthan the NIH-3T3 fibroblasts, the spreading morphologies of the hMSCswere imaged after 96 hours in culture, instead of the NIH-3T3fibroblasts' imaging time, after 24 h in culture). hMSCs growing on aflat glass plate (a), and on a 4 mm-(b), 3 mm-(c), 2 mm-(d), 1.1 mm-(e),900 nm-(f), 750 μm-(g), and 500 μm-(h) diameter glass ball are indicatedby the white arrows. Scale bars: 100 μm.

FIG. 20 shows cell length and width versus ball diameter for the hMSCs.The cell lengths and widths were measured for a number ofrandomly-selected cells (n_(hmMSCs)=240) growing on the flat glassplates and on the 4 mm-, 3 mm-, 2 mm-, 1.1 mm-, 950 μm-, 750 μm-, and500 μm-glass balls. 30 cells were measured for each ball diameterincluding the case of the flat glass plates, and the results shown aremean±SD.

FIG. 21 shows cell spread area versus ball diameter for the hMSCsmeasured in FIG. 20. The results shown are mean±SD. *: p<0.05; **:p<0.01; ***: p<0.001.

FIG. 22 shows the results for the cell lengths, cell widths, cell aspectratios, and cell spread areas of both the NIH-3T3 fibroblasts(n_(fibroblasts)=95) and hMSCs (n_(hmMSCs)=240) plotted in FIG. 17 andFIG. 20, and FIG. 18 and FIG. 21 are re-plotted together as single plotsfor the cell length (a), cell width (b), cell aspect ratio (c), and cellspread area (d) versus the ball diameter, respectively.

DETAILED DESCRIPTION OF THE DISCLOSURE

Several aspects of the disclosure are described below, with reference toexamples for illustrative purposes only. It should be understood thatnumerous specific details, relationships, and methods are set forth toprovide a full understanding of the disclosure. One having ordinaryskill in the relevant art, however, will readily recognize that thedisclosure can be practiced without one or more of the specific detailsor practiced with other methods, protocols, reagents, cell lines, andanimals. The present disclosure is not limited by the illustratedordering of acts or events, as some acts may occur in different ordersand/or concurrently with other acts or events. Furthermore, not allillustrated acts, steps, or events are required to implement amethodology in accordance with the present disclosure. Many of thetechniques and procedures described, or referenced herein, are wellunderstood and commonly employed using conventional methodology by thoseskilled in the art.

Unless otherwise defined, all terms of art, notations and otherscientific terms or terminology used herein are intended to have themeanings commonly understood by those of skill in the art to which thisdisclosure pertains. In some cases, terms with commonly understoodmeanings are defined herein for clarity and/or for ready reference, andthe inclusion of such definitions herein should not necessarily beconstrued to represent a substantial difference over what is generallyunderstood in the art. It will be further understood that terms, such asthose defined in commonly used dictionaries, should be interpreted ashaving a meaning that is consistent with their meaning in the context ofthe relevant art and/or as otherwise defined herein.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the disclosure.As used herein, the articles “a”, “an” and “the” should be understood toinclude plural reference unless the context clearly indicates otherwise.

The phrase “and/or,” as used herein, should be understood to mean“either or both” of the elements so conjoined, i.e., elements that areconjunctively present in some cases and disjunctively present in othercases.

As used herein, “or” should be understood to have the same meaning as“and/or” as defined above. For example, when separating a listing ofitems, “and/or” or “or” shall be interpreted as being inclusive, i.e.,the inclusion of at least one, but also including more than one, of anumber of items, and, optionally, additional unlisted items. Only termsclearly indicated to the contrary, such as “only one of” or “exactly oneof,” or, when used in the claims, “consisting of,” will refer to theinclusion of exactly one element of a number or list of elements. Ingeneral, the term “or” as used herein shall only be interpreted asindicating exclusive alternatives (i.e., “one or the other but notboth”) when preceded by terms of exclusivity, such as “either,” “oneof,” “only one of,” or “exactly one of.”

As used herein, the terms “including”, “includes”, “having”, “has”,“with”, or variants thereof, are intended to be inclusive similar to theterm “comprising.”

The term “surface curvature of a substrate” is used interchangeably withthe term “substrate curvature.”

In one aspect, the present disclosure provides methods of directing cellattachment and spreading on a substrate, comprising culturing a cell ona curved substrate in the presence of cell culture media, whereinattachment and spreading increases as the curvature of the substratedecreases. In a related aspect, the present disclosure provides apolyacrylamide (PA) gel embedded with curved substrates of variousdiameters to study cell mechanobiological responses to curvatures,patterns of various curvatures and other surface interface parameters.In yet another aspect, the disclosure provides methods of inducingisotropic spreading of cells, comprising culturing a cell on a curvedsubstrate, the curved substrate partially embedded in a gel surface,wherein the cell isotropically spreads over the curved substrate andonto the gel surface.

In the various described embodiments, the curved substrates for use inthe methods and kits described herein can range in size from about 1nanometer to about 10 millimeters. In one application, NIH-3T3 mousefibroblasts were cultured on glass balls having diameters ranging fromabout 5 micrometers to about 2 millimeters, and the cell morphologiesanalyzed by using an optical microscope and a 3D confocal laser scanningmicroscope. It was found that the fibroblasts are sensitive to thecurvatures of the balls, and there are significant differences in theattachment rates, migration speeds, and morphologies for cells culturedon glass balls of diameters at or below about 500 micrometers.

The curved substrates for use in the various described methods and kitsherein, whether all having the same shape or different shapes andwhether all having the same size or different sizes, will share thecharacteristic that they will have a curvature. The substrates can bedisposed within a gel or another material layer, to provide variousshapes, shape patterns, curvatures, and curvature patterns for cell andtissue culturing and for use in other surface and interfaceapplications. In some embodiments, the curved substrate comprises anarray or arrays of curved substrates, where in an array of curvedsubstrates, the shape and curvature and the material of each substratecan be same or can be different, and the pattern of the array can bewell-defined or can be random, and the patterns of two arrays can besame or can be different, and the arrangement or distribution of arrayscan be well-defined or can be random. The shapes can be predetermined byan ordered placement (e.g., uniform, periodic or symmetrical) of thecurved substrates or the curved substrates can be randomly distributedwithin the gel or another material layer to provide random shapes andpatterns. Both the ordered and random placement of the curved substrateswithin the gel or another material layer are important for use in celland tissue culturing and in other surface and interface applications.Curved substrates 49, see FIG. 5, can be disposed in a single patternwithin the gel or another material layer or can be disposed in clustersof several different patterns 50, 52, 54, and 56 across the surface of agel 58 as shown in FIG. 5. In lieu of patterned arrangements, the curvedsubstrates 49 can be placed randomly within the surface of the gel 58.

The curved substrates 49 for use in the various described methods andkits herein can exhibit any of the following shapes: ball-like,spherical, elliptical, oval, convex, concave, and combinations thereof.In some embodiments, the curved substrate is a spherical substrate, asshown in FIG. 5, such as, e.g., a ball. Any other defined or randomshapes having any curvature can also be utilized. The substrates canalso be solid or hollow, such as a spherical shell. In certainembodiments, the curved substrates comprise glass balls. The curves orshape of the substrates can be controlled to provide any predeterminedcurvature or, alternatively, the substrates can be formed to exhibitrandom curves and/or random shapes. In some embodiments, the curvedsubstrates have been illustrated and described as concave (i.e., havinga negative curvature) in shape. This is not necessarily required, asconvex (i.e., having a positive curvature) substrate shapes are alsouseful in the methods and kits described herein. Substrate shapes usefulin embodiments of the present disclosure are described in U.S. Pat. Nos.8,802,430 and 9,512,397, which are incorporated herein by reference.

In certain embodiments, the curved substrates have defined curvature. Incertain embodiments, these values may be random, while in otherembodiments, the values are not random but instead are defined based onthe application. Whether random or defined, the substrates arefabricated according to these parameters and then loaded into or onto amaterial layer, or alternatively provided in a liquid suspension (e.g.,cell culture media or buffer media) for use in cell or tissue culturingand in other surface and interface applications as described herein.

The curved substrate may also comprise a coating selected from the groupconsisting of a cell adhesive, a cell adhesion-promotor, a cellrepellent, or a combination thereof. The entire or part of the surfaceof the curved substrate can be coated or functionalized by a layer ofcell adhesives or cell adhesion-promotors, such as but not limited to,extracellular matrix proteins, fibronectin, collagen, laminin, etc. or alayer of cell repellents such as but not limited to, polyethylene glycol(PEG), etc., to promote or to inhibit the adhesion of the target ornon-target cell onto the curved substrate.

In specific embodiments, the curved substrate is a spherical substrate,wherein the attachment and spreading of cells increases as the diameterof the spherical substrate increases. For example, when the sphericalsubstrate comprises a diameter of between about 500 μm and about 6 mm,the attachment and spreading may be influenced in that both attachmentand spreading increases as the diameter of the spherical substrateincreases from about 500 μm to about 6 mm. Particularly useful forinducing isotropic spreading of cells, the spherical substrate may havea diameter of between about 5 μm and about 100 μm.

The curved substrates may be made of plastic, polydimethylsiloxane(PDMS), glass, silicon, or silicon nitride or any other materialsuitable for use in cell and tissue culturing or in any other surfaceinterface applications. Materials that will permit the culturing ofcells thereon, i.e., the material should preferably exhibit a curvature(convex or concave, or be able to change its shape in situ) and be ableto retain that curvature during cell/tissue culturing can also be used.Also, all the curved substrates utilized in any one cell culturingexperiment do not need to comprise the same material or the same shape.

FIGS. 1-4 illustrate substrate configurations and arrangements that areuseful in the methods and kits disclosed. FIG. 1 illustrates curvedsubstrates 10 embedded in a PA gel platform 14 for use in cell andtissue culturing and in other surface and interface applications in themethods and kits described herein. The PA gel platform is disposed on amaterial layer 15. In this platform, some cells 18 reside on the top ofthe curved substrates 10 while other cells 18A live on a surface 14A ofthe PA gel platform 14.

The extent to which the curved substrates are embedded in the gel can berandomly determined, for example, by simply dropping the curvedsubstrate onto an exposed surface of the gel. In another embodiment, thecurved substrates can be disposed such that an equal volume of eachsubstrate extends above the gel surface 14A or each substrate extends anequal distance above the gel surface 14A.

The gel platform 14 functions as both a soft material layer and anadhesive surface to prevent any sliding or rolling of the glass balls10. As can be seen in a scanning electron microscope (SEM) image of thisplatform (not shown), glass balls of 900 micrometers diameter, 500micrometers diameter, and below 300 micrometers diameters extend outfrom an upper surface of the PA gel platform 14.

FIG. 2 illustrates curved substrates 20 and 22 disposed in the PA gelplatform 14. An additional layer of gel material 28 is disposed on thesubstrate 20 and the cell 19A grows on the gel material 28. The cell 19Bgrows directly on the curved substrate 22 with no intervening layer ofgel material. FIG. 3 illustrates differently-shaped substrates 30 and 32disposed in the PA gel platform 14. An additional layer of gel material38 is disposed on the substrate 30 and the cell 19A grows on the gelmaterial 38. The cell 19B grows directly on the substrate 32 with nointervening layer of gel material.

FIG. 4 illustrates an embodiment without the gel platform layer. In thisembodiment, the curved substrates 40 are disposed on a material layer42. An adhesive material (not shown) affixes the substrates 40 to thematerial layer 42.

The use of a gel for embedding the curved substrate is not required foruse in the various described methods and kits herein. Any material layercan be used if it exhibits properties sufficient for receiving andretaining the substrate, such as relatively soft or deformable but yetsufficiently rigid to retain the substrate (e.g., glass balls) in placeduring cell/tissue culturing. For example, in lieu of the gel 58 of FIG.5, the material layer may comprise any other material such as glass,plastic, polydimethylsiloxane (PDMS), silica, silicon, silicon nitride,composite materials, transparent materials, non-transparent materials,or any other material suitable for use as the material layer in cell andtissue culturing or in any other surface interface applications. Thesubstrates may comprise the same material as the material layer andemerge or extend from the material layer to form curved structures forcell or tissue culturing or for use in other surface interfaceapplications.

In another aspect, the present disclosure provides methods of cellsorting, comprising culturing a mixed population of cell types, themixed population comprising a target cell and a non-target cell, on acurved substrate in the presence of cell culture media for a timesufficient for one of a target or a non-target cell to attach to thesubstrate; and removing, or separating, the cell culture media from thecurved substrate, wherein the target cell is contained either in thecell culture media or on the curved substrate, wherein the non-targetcell is contained in the cell culture media if the target cell iscontained on the curved substrate or the non-target cell is contained onthe curved substrate if the target cell is contained in the cell culturemedia.

The target cell type will be one cell type, while the non-target celltype can be one or more types. Non-limiting examples include: the targetcell can be a human mesenchymal stem cell (hMSC) and the non-targetcells can include, inter alia, a pool of NIH 3T3 fibroblasts and mousekidney fibroblasts; the target cell can be a hMSC and the non-targetcells can include a pool of NIH 3T3 fibroblasts and mouse kidneyfibroblasts and human umbilical vein endothelial cells (HUVEC); thetarget cell can be NIH 3T3 fibroblasts and the non-target cells caninclude a pool of hMSCs and human embryonic stem cells (hESC). In someembodiments, the non-target cell can attach to the curved substrate andthe target cell is present in the cell culture media. In an alternativeembodiment, the target cell can attach to the curved substrate and thenon-target cell is present in the cell culture media.

In embodiments comprising a spherical substrate, the substrate may havea diameter less than about 500 μm. In alternative embodiments, thespherical substrate comprises a diameter of about 300 μm or less. Infurther embodiments, the spherical substrate comprises a diametergreater than about 500 μm.

In some embodiments, the target cell is a stem cell. The stem cells mayinclude embryonic stem cells, tissue-specific stem cells, mesenchymalstem cells, and pluripotent stem cells. In at least one embodiment, thestem cell may be a mesenchymal stem cell.

In some embodiments, the mixed population of cell types comprises atleast stem cells and fibroblasts. In one particular embodiment, thefibroblasts attach to the curved substrate and the stem cells do notattach to the curved substrate. In an alternative embodiment, the stemcells attach to the curved substrate and the fibroblasts do not attachto the curved substrate.

Particularly useful in the cell sorting aspects described, the curvedsubstrate may comprise a coating selected from the group consisting of acell adhesive, a cell adhesion-promotor, a cell repellant, or acombination thereof. The entire or part of the surface of the curvedsubstrate can be coated or functionalized by a layer of cell adhesivesor cell adhesion-promotors, such as but not limited to, extracellularmatrix proteins, fibronectin, collagen, laminin, etc. or a layer of cellrepellents such as but not limited to, polyethylene glycol (PEG), etc.,to promote or to inhibit the adhesion of the target or non-target cellonto the curved substrate.

The methods of cell sorting involve culturing a mixed population of celltypes in the presence of cell culture media and one or more curvedsubstrate. The substrate may be bound or embedded, as described herein,or it may be suspended in cell culture media. Once either the target ornon-target cells are given sufficient time to bind the substrate, thesubstrate can be separated from the media; the target cell is containedeither in the cell culture media or on the curved substrate, wherein thenon-target cell is contained in the cell culture media if the targetcell is contained on the curved substrate or the non-target cell iscontained on the curved substrate if the target cell is contained in thecell culture media.

As one will understand from the provided disclosure herein, whether atarget cell or non-target cell binds the substrate will depend both onthe types of cells being separated and on the degree of curvature of thesubstrate. For example, the diameter ranges of the curved substrates(for spherical substrates) will dictate which cell types will attach andwhich will not attach. For example, hMSCs do not attach to the sphericalsubstrate if the diameter is about 300 μm or less. hMSCs may attach ifthe spherical substrate has a diameter greater than about 500 μm.Further, at least certain fibroblasts, such as NIH-3T3 cells, attach tospherical substrates great than about 58 μm.

In another aspect, the disclosure provides methods for guided inductionof stem cell differentiation, comprising culturing a stem cell on acurved substrate in the presence of cell culture media. As previouslydescribed herein, the curved substrate may be a convex substrate, aconcave substrate, a spherical substrate, an oval substrate, anelliptical substrate, or combinations thereof. The curved substrate canalso include a coating, such as a cell adhesive, a celladhesion-promotor, a cell repellent, or combinations thereof. The entireor part of the surface of the curved substrate can be coated orfunctionalized by a layer of cell adhesives or cell adhesion-promotors,such as but not limited to, extracellular matrix proteins, fibronectin,collagen, laminin, etc. or a layer of cell repellents such as but notlimited to, polyethylene glycol (PEG), etc., to promote or to inhibitthe adhesion of the target or non-target cell onto the curved substrate.Further, the coating can include one or more cell differentiationfactors to work in concert with the effects of the curved substrate onthe induction of differentiation. Differentiation induction factors orgrowth factors or soluble factors may be included in the media utilizedfor culturing the cells either concurrently in the presence of thecurved substrate, or, alternatively, before or after culturing of thecells on the curved substrate.

In embodiments comprising a spherical substrate, the spherical substratemay have a diameter of between about 500 μm and about 6 mm; betweenabout 500 μm and about 4 mm; between about 4 mm and about 6 mm; orbetween about 500 μm and about 2 mm. The diameter of the sphericalsubstrate that is utilized will depend on the type of stem cell that isbeing differentiated and/or the targeted type of differentiationresponse that is desired.

The stem cells that are being differentiated by the methods describedmay include embryonic stem cells, tissue-specific stem cells,mesenchymal stem cells, and pluripotent stem cells. In at least oneembodiment, the stem cell may be a mesenchymal stem cell. In someembodiments, the cell culture media may include osteocytedifferentiation induction media, whereby the stem cell differentiatesinto an osteocyte. In other embodiments, the methods result in the stemcell differentiating into an adipocyte.

In various other aspects, the present disclosure provides kits forperforming the methods described herein. A kit can comprise a curvedsubstrate and one or more containers comprising at least one reagent.Methods of the disclosure can be carried out using kits described hereinfor qualitatively or quantitatively sorting cells, directing cellattachment and/or spreading on a substrate, guiding stem celldifferentiation, or inducing isotropic spreading of cells.

In one aspect, the present disclosure provides kits for cell sorting,comprising a first reagent, wherein the first reagent comprises a curvedsubstrate. As previously described herein, the curved substrate can be aconvex substrate, a concave substrate, a spherical substrate, an ovalsubstrate, an elliptical substrate, or combinations thereof. When thesubstrate is a spherical substrate, the spherical substrate may includea diameter less than about 500 μm.

In further aspects, the disclosure provides kits for directing cellattachment and spreading on a substrate or inducing isotropic spreadingof cells, comprising a first reagent, wherein the first reagentcomprises a curved substrate as previously described herein. Inembodiments where the curved substrate is spherical, the diameter may bebetween about 500 μm and about 6 mm or between about 500 μm and about 2mm or between about 4 mm and about 6 mm or between about 4 mm and about6 mm. In some embodiments, the curved substrate is at least partiallyembedded in a gel surface for allowing a cell to isotropically spreadover the curved substrate and onto the gel surface.

In yet another aspect, the disclosure provides kits for guided inductionof stem cell differentiation, comprising a first reagent, wherein thefirst reagent comprises a curved substrate. In embodiments where thesubstrate is spherical, the substrate may have a diameter of betweenabout 500 μm and about 6 mm or between about 500 μm and about 2 mm orbetween about 4 mm and about 6 mm or between about 4 mm and about 6 mm.

The curved substrate in the kits disclosed above can be provided as acomponent of any structure herein described, such as for example, curvedsubstrates embedded in a gel surface, or as a plurality of curvedsubstrates suspended in a reagent. The reagent can be, for example, cellculture media. The kit can also contain a solid support such asmicrotiter multi-well plates, standards, assay diluent, wash buffer,adhesive plate covers, and/or instructions for carrying out a method ofthe disclosure using the kit. Likewise, the curved substrate can includeone or more coatings, such as a cell adhesive, a cell adhesion-promotor,a cell repellent, or a combination thereof. The entire or part of thesurface of the curved substrate can be coated or functionalized by alayer of cell adhesives or cell adhesion-promotors, such as but notlimited to, extracellular matrix proteins, fibronectin, collagen,laminin, etc. or a layer of cell repellents, such as but not limited to,polyethylene glycol (PEG), etc., to promote or to inhibit the adhesionof the target or non-target cell(s) onto the curved substrate. For thecell differentiation kits, the substrate may also include a coatingcontaining one or more cell-differentiation factor. Differentiationinduction factors or growth factors or soluble factors may be includedin the media utilized for culturing the cells either concurrently in thepresence of the curved substrate, or, alternatively, before or afterculturing of the cells on the curved substrate.

Kits of the disclosure include reagents for use in the methods describedherein, in one or more containers. The reagents can include cell culturemedia, cell-type detection or labelling agents, and stem celldifferentiation media. The kits may include specific internal controls,and/or probes, buffers, and/or excipients, separately or in combination.Each reagent can be supplied in a solid form or liquid buffer that issuitable for inventory storage. Kits may also include means forobtaining a sample from a host organism or an environmental sample, suchas for example components for extracting cell populations containingstem cells and/or fibroblasts.

Kits of the disclosure can be provided in suitable packaging. Suchpackaging materials include glass and plastic (e.g., polyethylene,polypropylene, and polycarbonate) bottles, vials, paper, plastic, andplastic-foil laminated envelopes and the like. In certain embodiments,the kit includes a microtiter tray with two or more wells and withreagents including primers, probes, specific internal controls, and/ormolecular beacons in the wells.

Kits of the disclosure may optionally include a set of instructions inprinted or electronic (e.g., magnetic or optical disk) form, relatinginformation regarding the components of the kits and/or how to makevarious determinations (e.g., substrate binding to target cells,comparison to control standards, etc.). The kit may also becommercialized as part of a larger package that includes instrumentationfor measuring other biochemical components.

Certain aspects of the disclosure provide the following non-limitingembodiments:

Embodiment 1

A method of cell sorting, comprising: culturing a mixed population ofcell types, the mixed population comprising a target cell and anon-target cell, on a curved substrate in the presence of cell culturemedia for a time sufficient for one of a target or a non-target cell toattach to the substrate; and removing, or separating, the cell culturemedia from the curved substrate, wherein the target cell is containedeither in the cell culture media or on the curved substrate, wherein thenon-target cell is contained in the cell culture media if the targetcell is contained on the curved substrate or the non-target cell iscontained on the curved substrate if the target cell is contained in thecell culture media.

Embodiment 2

The method of Embodiment 1, wherein the non-target cell attaches to thecurved substrate and the target cell is present in the cell culturemedia.

Embodiment 3

The method of Embodiment 1, wherein the target cell attaches to thecurved substrate and the non-target cell is present in the cell culturemedia.

Embodiment 4

The method of Embodiments 1-3, wherein the curved substrate comprises anarray or arrays of curved substrates.

Embodiment 5

The method of Embodiments 1-4, wherein the target cell is a stem cell.

Embodiment 6

The method of Embodiment 5, wherein the stem cell is a mesenchymal stemcell.

Embodiment 7

The method of Embodiments 1-6, wherein the curved substrate is selectedfrom the group consisting of a convex substrate, a concave substrate, aspherical substrate, an oval substrate, an elliptical substrate, andcombinations thereof.

Embodiment 8

The method of Embodiment 1, wherein the curved substrate is a sphericalsubstrate.

Embodiment 9

The method of Embodiment 8, wherein the spherical substrate is a ball.

Embodiment 10

The method of Embodiment 9, wherein the ball is a glass ball.

Embodiment 11

The method of Embodiment 8, wherein the spherical substrate comprises adiameter less than about 500 μm.

Embodiment 12

The method of Embodiment 1, wherein the mixed population of cell typescomprises stem cells and fibroblasts.

Embodiment 13

The method of Embodiment 1, wherein the mixed population of cell typesconsists of stem cells and fibroblasts.

Embodiment 14

The method of Embodiment 12, wherein the fibroblasts attach to thecurved substrate and the stem cells do not attach to the curvedsubstrate.

Embodiment 15

The method of Embodiment 13, wherein the fibroblasts attach to thecurved substrate and the stem cells do not attach to the curvedsubstrate.

Embodiment 16

The method of Embodiment 12, wherein the stem cells attach to the curvedsubstrate and the fibroblasts do not attach to the curved substrate.

Embodiment 17

The method of Embodiment 13, wherein the stem cells attach to the curvedsubstrate and the fibroblasts do not attach to the curved substrate.

Embodiment 18

The method of Embodiment 8, wherein the spherical substrate comprises adiameter of about 300 μm or less.

Embodiment 19

The method of Embodiments 1-18, wherein the curved substrate comprises acoating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.

Embodiment 20

The method of Embodiment 1, wherein the non-target cell type is one ormore cell types.

Embodiment 21

A kit for cell sorting, comprising: a first reagent, wherein the firstreagent comprises a curved substrate.

Embodiment 22

The kit of Embodiment 21, wherein the curved substrate is selected fromthe group consisting of a convex substrate, a concave substrate, aspherical substrate, an oval substrate, an elliptical substrate, andcombinations thereof.

Embodiment 23

The kit of Embodiments 21-22, wherein the curved substrate comprises aspherical substrate.

Embodiment 24

The kit of Embodiment 23, wherein the spherical substrate comprises adiameter less than about 500 μm.

Embodiment 25

The kit of Embodiments 21-24, wherein the curved substrate comprises acoating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.

Embodiment 26

A kit for cell sorting, comprising: a first reagent, wherein the firstreagent comprises a spherical substrate having a diameter less thanabout 500 μm.

Embodiment 27

The kit of Embodiment 26, wherein first reagent is immobilized on asolid support.

Embodiment 28

The kit of Embodiments 26-27, further comprising a second reagent,wherein the second reagent comprises cell culture media.

Embodiment 29

The kit of Embodiments 26-28, further comprising a third reagent,wherein the third reagent comprises a detection or labelling agent.

Embodiment 30

The kit of Embodiments 26-29, wherein the spherical substrate comprisesa coating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.

Embodiment 31

A method of directing cell attachment and spreading on a substrate,comprising: culturing a cell on a curved substrate in the presence ofcell culture media, wherein attachment and spreading increases as thecurvature of the substrate decreases.

Embodiment 32

The method of Embodiment 31, wherein the curved substrate is selectedfrom the group consisting of a convex substrate, a concave substrate, aspherical substrate, an oval substrate, an elliptical substrate, andcombinations thereof.

Embodiment 33

The method of Embodiments 31-32, wherein the curved substrate comprisesa coating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.

Embodiment 34

The method of Embodiments 32-33, wherein the curved substrate is aspherical substrate, wherein the attachment and spreading increases asthe diameter of the spherical substrate increases.

Embodiment 35

The method of Embodiment 34, wherein the spherical substrate comprises adiameter of between about 500 μm and about 6 mm, wherein attachment andspreading is influenced in that both attachment and spreading increasesas the diameter of the spherical substrate increases from about 500 μmto about 6 mm.

Embodiment 36

A kit for directing cell attachment and spreading on a substrate,comprising: a first reagent, wherein the first reagent comprises acurved substrate.

Embodiment 37

The kit of Embodiment 36, wherein the curved substrate is selected fromthe group consisting of a convex substrate, a concave substrate, aspherical substrate, an oval substrate, an elliptical substrate, andcombinations thereof.

Embodiment 38

The kit of Embodiments 36-37, wherein the curved substrate comprises acoating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.

Embodiment 39

The kit of Embodiment 36, wherein the curved substrate is a sphericalsubstrate.

Embodiment 40

The kit of Embodiment 39, wherein the spherical substrate comprises adiameter of between about 500 μm and about 6 mm.

Embodiment 41

The kit of Embodiments 36-40, wherein first reagent is immobilized on asolid support.

Embodiment 42

The kit of Embodiments 36-41, further comprising a second reagent,wherein the second reagent comprises cell culture media.

Embodiment 43

The kit of Embodiment 42, wherein the cell culture media is a culturemedia that induces stem cell differentiation.

Embodiment 44

The kit of Embodiments 36-44, further comprising a third reagent,wherein the third reagent comprises a cell-type detection agent.

Embodiment 45

The kit of Embodiment 39, wherein the spherical substrate comprises adiameter of between about 500 μm and about 2 mm.

Embodiment 46

The kit of Embodiment 39, wherein the spherical substrate comprises adiameter of between about 2 mm and about 4 mm.

Embodiment 47

The kit of Embodiment 39, wherein the spherical substrate comprises adiameter of between about 4 mm and about 6 mm.

Embodiment 48

A method for guided induction of stem cell differentiation, comprising:culturing a stem cell on a curved substrate in the presence of cellculture media.

Embodiment 49

The method of Embodiment 48, wherein the curved substrate comprises acoating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.

Embodiment 50

The method of Embodiments 48-49, wherein the curved substrate isselected from the group consisting of a convex substrate, a concavesubstrate, a spherical substrate, an oval substrate, an ellipticalsubstrate, and combinations thereof.

Embodiment 51

The method of Embodiment 48, wherein the curved substrate is a sphericalsubstrate.

Embodiment 52

The method of Embodiment 51, wherein the spherical substrate comprises adiameter of between about 500 μm and about 4 mm.

Embodiment 53

The method of Embodiment 51, wherein the spherical substrate comprises adiameter of between about 500 μm and about 2 mm.

Embodiment 54

The method of Embodiment 51, wherein the spherical substrate comprises adiameter of between about 4 mm and about 6 mm.

Embodiment 55

The method of Embodiment 51, wherein the spherical substrate comprises adiameter of between about 500 μm and about 6 mm.

Embodiment 56

The method of Embodiment 48, wherein the stem cell is a mesenchymal stemcell.

Embodiment 57

The method of Embodiment 56, wherein the cell culture media comprisesosteocyte differentiation induction media, whereby the stem celldifferentiates into an osteocyte.

Embodiment 58

The method of Embodiment 56, wherein the stem cell differentiates intoan adipocyte.

Embodiment 59

A kit for guided induction of stem cell differentiation, comprising: afirst reagent, wherein the first reagent comprises a curved substrate.

Embodiment 60

The kit of Embodiment 59, wherein the curved substrate is selected fromthe group consisting of a convex substrate, a concave substrate, aspherical substrate, an oval substrate, an elliptical substrate, andcombinations thereof.

Embodiment 61

The kit of Embodiments 59-60, wherein the curved substrate comprises acoating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.

Embodiment 62

The kit of Embodiment 59, wherein the curved substrate is a sphericalsubstrate.

Embodiment 63

The kit of Embodiment 62, wherein the spherical substrate comprises adiameter of between about 500 μm and about 6 mm.

Embodiment 64

The kit of Embodiments 59-63, wherein first reagent is immobilized on asolid support.

Embodiment 65

The kit of Embodiments 59-64, further comprising a second reagent,wherein the second reagent comprises cell culture media.

Embodiment 66

The kit of Embodiment 65, wherein the cell culture media is a culturemedia that induces stem cell differentiation.

Embodiment 67

The kit of Embodiments 59-66, further comprising a third reagent,wherein the third reagent comprises a cell-type detection agent.

Embodiment 68

The kit of Embodiment 62, wherein the spherical substrate comprises adiameter of between about 500 μm and about 2 mm.

Embodiment 69

The kit of Embodiment 62, wherein the spherical substrate comprises adiameter of between about 2 mm and about 4 mm.

Embodiment 70

The kit of Embodiment 62, wherein the spherical substrate comprises adiameter of between about 4 mm and about 6 mm.

Embodiment 71

A method of inducing isotropic spreading of cells, comprising: culturinga cell on a curved substrate, the curved substrate partially embedded ina gel surface, wherein the cell isotropically spreads over the curvedsubstrate and onto the gel surface.

Embodiment 72

The method of Embodiment 71, wherein the curved substrate comprises acoating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.

Embodiment 73

The method of Embodiment 71, wherein the curved substrate is a sphericalsubstrate.

Embodiment 74

The method of Embodiment 73, wherein the spherical substrate comprises adiameter of between about 5 μm and about 100 μm.

Embodiment 75

The method of Embodiment 71, wherein the curved substrate is selectedfrom the group consisting of a convex substrate, a concave substrate, aspherical substrate, and combinations thereof.

Embodiment 76

A kit for inducing isotropic spreading of cells, comprising: a firstreagent, wherein the first reagent comprises a curved substrate.

Embodiment 77

The kit of Embodiment 76, wherein the curved substrate is at leastpartially embedded in a gel surface, for allowing a cell toisotropically spread over the curved substrate and onto the gel surface.

Embodiment 78

The kit of Embodiment 76, wherein the curved substrate is selected fromthe group consisting of a convex substrate, a concave substrate, aspherical substrate, and combinations thereof.

Embodiment 79

The kit of Embodiments 76-78, wherein the curved substrate comprises acoating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.

Embodiment 80

A method of inducing isotropic spreading of cells, comprising: culturinga cell on a curved substrate, the curved substrate immobilized on amaterial layer, wherein the cell isotropically spreads over the curvedsubstrate and onto the material layer.

Embodiment 81

The method of Embodiment 80, wherein the curved substrate is a sphericalsubstrate.

Embodiment 82

The method of Embodiment 81, wherein the spherical substrate comprises adiameter of between about 5 μm and about 100 μm.

Embodiment 83

The method of Embodiment 80, wherein the curved substrate is selectedfrom the group consisting of a convex substrate, a concave substrate, aspherical substrate, an oval substrate, an elliptical substrate, andcombinations thereof.

Embodiment 84

The method of Embodiment 83, wherein the curved substrate is a sphericalsubstrate.

Embodiment 85

The method of any of Embodiments 80-84, wherein the curved substratecomprises a coating selected from the group consisting of a celladhesive, a cell adhesion-promotor, a cell repellent, or a combinationthereof.

The methods and devices herein described and the related kits arefurther illustrated in the following examples, which are provided by wayof illustration and is not intended to be limiting. It will beappreciated that variations in proportions and alternatives in elementsof the components shown will be apparent to those skilled in the art andare within the scope of embodiments of the present disclosure.Theoretical aspects are presented with the understanding that Applicantdoes not seek to be bound by the theory presented. All percentages,unless otherwise specified, are by weight, and all solvent mixtureproportions are by volume unless otherwise noted.

All publications and patent documents cited in this application areincorporated by reference in pertinent part for all purposes to the sameextent as if each individual publication or patent document were soindividually denoted. By citation of various references in thisdocument, Applicants do not admit any particular reference is “priorart” to their invention.

EXAMPLES

The methods, devices, and related kits herein described are furtherillustrated in the following examples, which are provided by way ofillustration and are not intended to be limiting. It will be appreciatedthat variations in proportions and alternatives in elements of thecomponents shown will be apparent to those skilled in the art and arewithin the scope of aspects and embodiments of the present disclosure.Theoretical aspects are presented with the understanding that Applicantsdo not seek to be bound by the theory presented. All parts or amounts,unless otherwise specified, are by weight.

The following materials and methods were used for the methods anddevices exemplified in Example 1 herein.

RT-PCR Analysis—

To check the differentiation responses of the hMSCs growing on the glassballs, RT-PCR analysis was conducted to quantify the relative geneexpression of these hMSCs. After 11 days of growing on the glass ballsof the hMSCs in the above-mentioned growth media, the glass balls withthe hMSCs attached were extracted with tweezers and put into a 1.5 mlepi tube. The time 11 days is long enough for the differentiation geneexpression of the hMSCs to occur in accordance with the relevant timeframes reported in the literature (Engler et al., 2006; Viswanathan etal., 2015; Kilian et al., 2010). 1 ml of Trizol (TriReagent, MolecularResearch Center TR118, Cincinnati, Ohio) was added to the epi tube for0.5-1×106 cells to lyse the cell membrane. To separate the phases, 0.2ml of chloroform (Sigma-Aldrich C2432, St. Louis, Mo.) was added intothe tube. After shaken vigorously, the tube was centrifuged at 12,000rpm and 4° C. for 20 min. The top clear aqueous phase layer containingRNA was then transferred to a new 1.5 mL epi tube. To precipitate theRNA, 0.5 ml of isopropyl alcohol (Sigma-Aldrich 19516, St. Louis, Mo.)was added into the tube. After inverted several times, the tube wasincubated at room temperature for 20 min and then was centrifuged at12,000 rpm and 4° C. for 20 min. The solution was slowly poured out withthe help of a pipette. To wash the pellet of the RNA, 1 ml of 75%ethanol (Sigma-Aldrich E7023, St. Louis, Mo.) was added into the tube,and then the tube was centrifuged at 12,000 rpm and 4° C. for 20 min.The ethanol was slowly poured out with the help of a pipette, and then16 μL of DNAse-RNAse free water (DEPC water, VWR IC821739, Radnor, Pa.)was added into the tube to dissolve the RNA pellet. The tube was left ona heat block at 55° C. for 5 min for the pellet to become invisible.

The quality and concentration of the RNA samples were then assessed byusing a spectrophotometer (NanoDrop LITE, Thermo Scientific ND-NDL,Waltham, Mass.). To assess the purity of an RNA sample, one mustevaluate the value of A260/A280 following the spectrophotometer reading.The value of A260/A280 should be greater than 2.0 if the RNA sample ispure enough. Lower values indicate the presence of contaminants such assalts, carbohydrates, peptides, and proteins. In order to reveal thedifferences in the relative gene expression results of the hMSCs growingon the glass balls with different diameters, it is critical to use thesame amount of the corresponding RNA sample in each cDNA synthesisreaction, which was conducted by using the iScript cDNA Synthesis Kit(Bio-RAD 170, Hercules, Calif.) according to the manufacturer'sinstruction. The complete cDNA reaction mix (total volume: 20 μL) wasincubated in a thermal cycler (T100, Bio-RAD 1861096, Hercules, Calif.)by using a protocol recommended by the manufacturer.

The quantitative PCR (qPCR) reaction mix (total volume: 20 μL) consistsof an appropriate amount of the synthesized cDNA (1-4 μL), a selectedprimer (1 μL) to target the specific type of gene expression, theSsoAdvanced Universal SYBR Green Supermix (Bio-RAD 172, Hercules,Calif.) (10 μL), and nuclease-free water. The qPCR reaction mix wasloaded into an RT-PCR instrument (CFX Connect Real-Time System, Bio-RAD1855200, Hercules, Calif.), and the instrument was programmed to run thereaction mix according to the following thermal cycling protocolrecommended by the manufacturer: activation at 95° C. for 2 min, thendenaturation at 95° C. for 5 sec and annealing/extension at 60° C. for30 sec for 40 cycles. In the experiment, 18S rRNA (18S ribosomal RNA)was used as the housekeeping gene. The gene expression data wereanalyzed by using the method, and the gene expression result of thehMSCs growing on the flat glass plates was used as the control tocompute the relative gene expression results of the hMSCs growing on theglass balls with different diameters.

The following materials and methods were used for the methods anddevices exemplified in Examples 2-4 herein.

Preparation of the Micro Glass Ball Embedded Polyacrylamide (PA) Gels—

The micro glass ball embedded PA gels were prepared by using theprotocol described by the inventor earlier (Lee and Yang, 2012)(incorporated herein by reference in its entirety), and the Young'smodulus of a PA gel was determined by using the protocol of Wang andPelham on the PA gel preparation (Wang and Pelham, 1998). PA gels with awide range of the Young's modulus can be prepared by adjusting theconcentrations of acrylamide and bis-acrylamide (the cross-linker) inthe final PA solution. For the presented study, the final concentrationsof 8% w/v acrylamide and 0.08% w/v bis-acrylamide were used to form thePA gels with the Young's modulus of 75 kPa, the final concentrations of8% w/v acrylamide and 0.02% w/v bis-acrylamide were used to form the PAgels with the Young's modulus of 10 kPa, and the final concentrations of3% w/v acrylamide and 0.10% w/v bis-acrylamide were used to form the PAgels with the Young's modulus of 1 kPa. To prepare the PA gels with oneof the above-mentioned three Young's moduli, the PA solution with afinal volume of 5,000 μL was prepared by mixing appropriate amounts ofthe 40% w/v acrylamide stock solution and the 2% w/v bis-acrylamidestock solution with deionized water, and then the PA solution wasdegased by vacuuming for 20 minutes. To polymerize the PA solution, 30μL of N,N,N′,N′-tetramethyl-ethylenediamine (TEMED, Fisher BioReagentsBP150-20, Pittsburgh, Pa.) was added to the PA solution. The PA solutionwas then immediately divided into five 15 mL tubes as 1,000 μL per tube.After 11 μL of 10% ammonium persulfate (Electrophoresis, FisherBioReagents BP179-25, Pittsburgh, Pa.) was added to each tube of the PAsolution, the PA solution started to polymerize within one min, and thispolymerization process finished in about 24 hours.

Before the polymerization process started, 100 μL of the PA solution waspipetted onto the bottom of a 35 mm-diameter cell culture dish, and thenan appropriate amount of the micro glass balls with diameters of mixed5-100 μm (3M Glass bubbles K-20, St. Paul, Minn.) was immediatelydropped onto the PA solution. A 22 mm-diameter glass coverslip was thencarefully placed on the top of the PA solution to evenly press the microglass balls into the unpolymerized PA solution. After the polymerizationprocess of the PA solution completed in about 24 hours, the micro glassball embedded PA gel was formed. The surface of the micro glass ballembedded PA gel was then coated with the cell adhesive protein,fibronectin (Sigma-Aldrich F8141-1MG, St. Louis, Mo.).

Cell Culture—

NIH-3T3 mouse embryo fibroblasts (ATCC CRL-1658, Manassas, Va.) werecultured, on the above-prepared micro glass ball embedded PA gels in thecell culture dishes, in Dulbecco's Modified Eagle Medium (DMEM, ATCC30-2002, Manassas, Va.) with 10% Calf Bovine Serum (ATCC 30-2030,Manassas, Va.) and 1% Penicillin-Streptomycin (MP biomedicals no.091670049, Solon, Ohio). The fibroblasts were incubated at 37° C. with ahumidified 5% CO₂ atmosphere, and the culture medium was changed twiceper week.

Imaging Analysis—

Phase-contrast images of the cells wrapping over the micro glass ballsin the above cell culture were taken by an upright light microscope(Axioskop 2 plus, Carl Zeiss, Germany) using 10× and 40× objectives. Thephase-contrast images were manually outlined to define the boundaries ofthe cells to measure the spread areas of the cells by using the softwareImageJ.

The following materials and methods were used for the methods anddevices exemplified in Examples 5-8 herein.

Treatment of Glass Coverslips—

In a micro glass ball embedded gel for the purpose of this study, theupper parts of many of the micro glass balls are exposed from the topsurface of the gel. When a micro glass ball embedded gel experimentalplatform is prepared, the platform is subjected to the perturbingfluidic shear forces of the gel solution and phosphate buffered saline(PBS) during the handlings and transportations of the platform. When theplatform is used for cell culturing, the platform is subjected to theperturbing fluidic shear forces of the culture media during thehandlings and transportations of the culture dish, loaded with theplatform, in the entire cell culturing, treatment, observation, andimaging process. These inevitable perturbing fluidic shear forces inducerolling and detaching of the embedded micro glass balls from the gel.Thus, the most important issue of using a micro glass ball embedded PAgel experimental platform for cell studies is how to reduce the rollingand detaching of the embedded micro glass balls from the PA gel duringthe entire this platform-related experimental process.

It is well known that a polymer network swells at temperatures higherthan the room temperature and shrinks at temperatures lower than theroom temperature (Tanaka et al., 1992). A PA gel shrinks in water atsufficiently low temperatures and swell at higher temperatures, slowlyand reversibly. The extents of the shrinking and swelling and theinverting temperatures between these two processes depend on the gelcomposition (Hirotsu, 1987; Beltran et al., 1991). It was observed thatthe PA gels were significantly swollen at 37° C. in the incubatorcompared with the same PA gels at room temperature, and these volumechanges of the PA gels loosened the adhesion between the embedded microglass balls and the PA gel materials, and then the embedded micro glassballs became much more susceptible to the above-mentioned perturbingfluidic shear forces that drove the rolling and detaching of theembedded micro glass balls from the PA gels during the entire cellculturing process. Thus, to reduce the rolling and detaching of theembedded micro glass balls from a PA gel, the volume change of the PAgel during the entire experimental process needs to be reduced as muchas possible.

In order to reduce the volume changes of the PA gels, glass coverslipswere treated with allytrichlorosilane (ATCS) to present vinyl groups onthe surfaces of the glass coverslips to promote and strengthen theattachment of the PA gels to the glass coverslips. The vinyl groups inATCS react with the acrylamide during the free radical polymerization ofthe PA solution, and then the PA gels adhere strongly to the ATCSfunctionalized surfaces of the glass coverslips by covalent bindings(Buxboim et al., 2010). This strong adherence of the PA gels to the ATCStreated glass coverslips will ensure the volume changes of the PA gelsto be minimum during the entire experimental process, and thus the PAgels can hold the micro glass balls tightly and any rolling anddetaching of the embedded micro glass balls from the PA gels areminimized. A brief introduction of the ATCS treating process on theglass coverslips is as follows.

Glass coverslips of 22 mm in diameter were boiled in ethanol for 10minutes, rinsed in distilled water (DW), and immersed in RCA at 80° C.for 10 minutes. RCA consists of DW, hydrogen peroxide (30%, FisherBioReagents BP2633-500, Pittsburgh, Pa.), and ammonium hydroxide (29%,Fisher BioReagents S93120A, Pittsburgh, Pa.) at a volume ratio of 3:1:1.The RCA-treated glass coverslips were rinsed in DW, ethanol (FisherBioReagents A407-1, Pittsburgh, Pa.), and chloroform (Fisher BioReagentsAC15821-0010, Pittsburgh, Pa.), and silanized in 0.1% ATCS (95%, FisherBioReagents AC31322-0050, Pittsburgh, Pa.) in chloroform with 0.1%triethylamine (TEA, 99.7%, Fisher BioReagents AC21951-0050, Pittsburgh,Pa.) for 30 min. The ATCS treated glass coverslips were subsequentlyrinsed in chloroform, ethanol, and DW, and then these coverslips wereimmediately used for the preparation of the micro glass ball embedded PAgels on their top surfaces.

Preparation of PA Gels—

Due to their smaller volume changes, the more rigid PA gels can also doa better job than the relatively softer PA gels in reducing the rollingand detaching of the embedded micro glass balls from the PA gels duringthe entire experimental process. To make the more rigid PA gels (Lee andYang, 2012; Wang and Pelham, 1998), a 1500 μL of acrylamide solution(40%/electrophoresis, Fisher BioReagents BP1402-1, Pittsburgh, Pa.) anda 700 μL of bis-acrylamide solution (2%/electrophoresis, FisherBioReagents BP1404-250, Pittsburgh, Pa.) were mixed in a 2750 μL ofdeionized water with a 50 μL of HEPES buffer solution (1M/pH7.3, FisherBioReagents BP299-100, Pittsburgh, Pa.) to form the PA solution. Thetotal volume of 5,000 μL of the PA solution was de-gassed by vacuumingfor 20 minutes. To polymerize the PA solution, a 30 μL ofN,N,N′,N′-tetramethyl-ethylenediamine (TEMED, Fisher BioReagentsBP150-20, Pittsburgh, Pa.) was added to the PA solution. Then the PAsolution was immediately divided into five 15-mL tubes as 1,000 μL pertube. After adding an 11 μL of 10% ammonium persulfate (Electrophoresis,Fisher BioReagents BP179-25, Pittsburgh, Pa.) to each tube of the PAsolution, the PA solution starts to polymerize within one min, and thispolymerization process finishes in about 24 hours. After thepolymerization process is finished, the formed PA gels should haveelastic moduli that are much larger than 100 kPa according to Wang andPelham's protocol (Wang and Pelham, 1998) for the concentrations of theacrylamide solution and bis-acrylamide solution used here.

Before the polymerization process starts, a volume of the PA solution,depending on the diameters of the glass balls to be embedded, waspipetted onto an ATCS treated glass coverslip lying on the bottom of a35 mm-diameter cell culture dish. Depending on the desired studies,appropriate amounts or combination of the micro glass balls withdiameters of mixed 5-100 μm, mixed 50-300 μm, 500 μm, 750 μm, 900 μm,1.1 mm, 2 mm, 3 mm, and 4 mm (Blockheadstamps, Portland, Oreg.) wereimmediately dropped onto the PA solution. A 22 mm-diameter glasscoverslip was then carefully placed on the top of the PA solution toevenly press the glass balls into the unpolymerized PA solution. Thepolymerization process of the PA solution completed in about 24 hours,and the micro glass ball embedded PA gel, which was attached to the ATCStreated glass coverslip, was formed. The formed micro glass ballembedded PA gel was rinsed with PBS twice in the following 24 hours.After removing all the PBS in the cell culture dish, the micro glassball embedded PA gel was dried in air and exposed to the ultravioletradiation existing in the cell culture hood for 2 hours forsterilization.

Cell Culture—

NIH-3T3 mouse embryo fibroblasts (ATCC CRL-1658, Manassas, Va.) werecultured, in the cell culture dishes loaded with the glass coverslipswith the above-prepared micro glass ball embedded PA gels attached, inDulbecco's Modified Eagle Medium (DMEM, ATCC 30-2002, Manassas, Va.)with 4500 mg/L glucose, 4 mM L-glutamine, 1 mM sodium pyruvate, and 1500mg/L sodium bicarbonate, and the DMEM was supplemented with 10% CalfBovine Serum (ATCC 30-2030, Manassas, Va.) and 1%Penicillin-Streptomycin (MP biomedicals no. 091670049, Solon, Ohio). Thefibroblasts were incubated at 37° C. with a humidified 5% CO₂atmosphere, and the culture medium was changed twice per week.

hMSCs (ATCC PCS-500-011, Manassas, Va.) were cultured, also in the cellculture dishes loaded with the glass coverslips with the above-preparedmicro glass ball embedded PA gels attached, in Mesenchymal Stem CellBasal Media (ATCC PCS-500-030, Manassas, Va.) plus one Mesenchymal StemCell Growth Kit (ATCC PCS-500-040, Manassas, Va.) that contains thefollowing growth supplements: MSC Supplement (composed of FB S, rh FGFbasic, rh FGF acidic, and rh EGF) and L-alanyl-L-glutamine.Gentamicin-Amphotericin B Solution (ATCC PCS-999-025, Manassas, Va.)with Penicillin-Streptomycin-Amphotericin B Solution (ATCC PCS-999-002,Manassas, Va.) was also added to the basal media. The hMSCs wereincubated at 37° C. with a humidified 5% CO₂ atmosphere, and the culturemedium was changed twice per week.

For comparisons, the above two cell types were also cultured on the flatglass plates, 22 mm-square glass coverslips.

Image Analysis—

Phase-contrast images of the cells adhered to the micro glass balls andthe flat glass plates in the above cell culture were taken by an uprightlight microscope (Axioskop 2 plus, Carl Zeiss, Germany) using a 10×objective. The phase-contrast images were manually outlined to definethe boundaries of the cells to measure the lengths, widths, and spreadareas of the cells by using the software Photoshop (Adobe SystemsIncorporated, San Jose, Calif.) and the software ImageJ (available athttp://rsb.info.nih.gov.ij/).

By using the enlarged phase-contrast image of a cell, the boundary ofthe cell nucleus was reasonably-accurately outlined by an oval. Theex-rectangle of this oval was then sketched, and the four sides of thisex-rectangle were tangent to the oval, the length direction of thisex-rectangle was parallel to the long axis of the oval, and the widthdirection of this ex-rectangle was parallel to the short axis of theoval. This ex-rectangle was then enlarged with the aspect ratiounchanged to just enclose the entire boundary of the cell. In thispaper, the length of this enlarged ex-rectangle was the measure of thecell length. In the directions that are perpendicular to the direction(i.e., the length direction of the ex-rectangle) that measured the celllength, the maximum straight-line distance from one side of the cellboundary to the other side of the cell boundary across the cell body wasthe measure of the cell width. This method of defining/measuring thelength and width of a cell should be a reasonable method to quantify thedimensions of the cell.

The aspect ratio of the cell was then calculated from the measuredlength and width of the cell and calculated as cell width/length, andthe spread area of the cell was measured as the total area enclosed bythe boundary of the cell.

Statistical Analysis—

The measured data, including the cell lengths, widths, aspect ratios,and spread areas, were shown as mean±standard deviation (SD) for eachball diameter. The significance or insignificance of differences betweenthe means of the measured spread areas of the cells growing on the glassballs with different diameters were tested by performing the one-wayanalysis of variance (ANOVA) with Tukey's post hoc test for multiplecomparisons by the software SPSS Statistics (International BusinessMachines (IBM) Corp., Armonk, N.Y.).

Example 1 Stem Cell Differentiation Responses to Substrate Curvatures

Since the mean cell spreading area decreases with the increase of thesubstrate curvature, the cell contractility decreases with the increaseof the substrate curvature. Therefore, it was hypothesized that thecurvature of the substrate on which a stem cell is growing guides thedifferentiation of the stem cell. Adipose-derived human mesenchymal stemcells (hMSCs) were utilized in the experiments described below, sincethey are capable of differentiation into various cell types based on thetype of differentiation media utilized (see FIG. 6).

hMSCs were cultured without differentiation induction media on the microglass ball embedded PA gels in the stem cell basal media with growth kitfor 11 days before analyzing gene expression (see FIG. 7). Therefore,since no differentiation-induction chemical media was added (involved),the differentiation results are due to substrate curvatures only, asillustrated in FIG. 8.

hMSCs were also cultured with adipocyte differentiation induction mediaon the micro glass ball embedded PA gels in the stem cell basal mediawith growth kit for 48 hours. Media was then replaced and incubated withadipocyte differentiation initiation media for 48 hours, and then mediawas replaced and incubated with adipocyte differentiation maintenancemedia for 7 days before analyzing gene expression (see FIG. 7).

According to ATCC's protocol, if the hMSCs were growing in a basalmedium with growth kit only (i.e., no corresponding differentiationinduction media were added to the growth media), the hMSCs growing onthe flat plates should not be differentiating. The relative geneexpressions of the hMSCs growing on the balls with different diameterswere then computed with respect to the corresponding gene expression ofthe hMSCs growing on the flat plates. In FIG. 7, as shown by theexpression results of the gene PPARG, an indicator of adipogenesis, thehMSCs growing on the balls with diameters of 500 μm, 750 μm, 900 μm, and1.1 mm had significant adipogenesis after 11 days, whereas the hMSCsgrowing on the balls with diameters of 2 mm, 3 mm, and 4 mm, and on theflat plates had negligible adipogenesis. Therefore, the adipogenesis ofthe hMSCs can be induced purely by the curvatures of the substrates onwhich these stem cells are growing.

hMSCs were also cultured with osteocyte differentiation induction mediaon the micro glass ball embedded PA gels in the stem cell basal mediawith growth kit for 48 hours. Media was then replaced and incubated withosteocyte differentiation media for 9 days before analyzing geneexpression (see FIG. 7). Results are shown in FIG. 9.

The qPCR results showed that adipogenesis can be induced purely by thesubstrate curvatures, i.e., the surface curvatures of the smaller glassballs. With the adipocyte differentiation induction media, the levels ofthe relative adipogenic gene expression are elevated for the hMSCsgrowing on the surfaces of the smaller glass balls. With the osteocytedifferentiation induction media, the levels of the relative osteogenicgene expression of the hMSCs decreased with the decrease of thesubstrate ball diameter from 6 mm to 3 mm, and increased with thedecrease of the substrate ball diameter from 3 mm to 500 μm.

In the present disclosure, hMSCs were cultured on the micro glass ballswhose surfaces are curved and curvature-defined, and the spreading ofthe stem cells on the glass balls were natural. Since as shown in FIG.6, the mean cell spread area of the hMSCs decreases with the decrease ofthe substrate ball diameter, the curvature of the substrate restrictedthe spreading of the hMSCs. According to the gene expression results,shown in FIG. 7, of the hMSCs growing on the balls, without thecorresponding differentiation induction media, the adipogenesis of thehMSCs can be induced by the curvature of a substrate on which the stemcells are growing. This shows that curvature-alone can induce stem celldifferentiation.

The cell experiments demonstrate that the class of substrates, microglass ball embedded gels, described by this disclosure is a very usefuland powerful tool for studying cell mechanobiological responses tosubstrate curvatures and local substrate stiffness, and for related celland tissue engineering and biomedical applications. The related detailedand systematic studies on the effects of substrate curvatures on thedifferentiations of stem cells will have applications in tissueengineering and regenerative medicine, which may result in a newdirection of research and development in stem cell biology and stem cellengineering/technology.

Example 2 Wrapping Over a Ball Realizes Cell Natural Isotropic-Spreading

FIG. 10 is a schematic illustration of the speculated differentconfigurations of a cell wrapping over a micro glass ball embedded onthe surface of a PA gel. For the configurations of Cells 1 and 2, abouthalf of each of the embedded micro glass balls (i.e., Balls 1 and 2) isabove the gel surface, and the micro glass ball (Ball 1) on which Cell 1is growing is much larger than the micro glass ball (Ball 2) on whichCell 2 is growing. Then, the spread area of Cell 1 on the surface ofBall 1, estimated as πD² _(Ball 1)/2, i.e., the half of the entiresurface area of Ball 1, where D_(Ball 1) is the diameter of Ball 1, ismuch larger than that of Cell 2 on the surface of Ball 2, estimated asπD² _(Ball 2)/2, i.e., the half of the entire surface area of Ball 2,where D_(Ball 2) is the diameter of Ball 2. Since Cells 1 and 2 are thesame type of cells, they have similar stretching/spreading potential.Then, Cell 2 should have a much larger further spreading potential onthe gel surface after wrapping over Ball 2 than Cell 1 after wrappingover Ball 1. Therefore, the relative spreading on the gel surface ofCell 2 with respect to the size of Ball 2 should be significantly largerthan that of Cell 1 with respect to the size of Ball 1. But this largershould be just “significantly larger” not “much larger” because that,the Young's modulus of the glass material is about six orders ofmagnitude higher than that of the most rigid PA gel material used here,cells spread and migrate according to the distribution of the rigidityof a substrate (Lo et al., 2000; Discher et al., 2005), and then thespreading potential on the gel surface of the cells is much smaller thanthat on the glass balls. Thus, the total spread area, the spread area onthe glass ball plus the spread area on the gel surface, of Cell 1 shouldstill be much larger than that of Cell 2.

Cell 3 in FIG. 10 is growing on a micro glass ball which only has asmall bottom part embedded in the gel, and this small bottom part isless than half of the entire ball. Cell 3 wrapped over the top half ofthe micro glass ball, extended straightly down to the gel surface, andfurther spread on the gel surface. Before Cell 3 reached thisenergetically-favorable position, it is assumed that the cell hadextended and searched around to reach to and anchor on the gel surfaceand had rearranged its anchoring locations on the gel surface. Cell 4 inFIG. 10 is growing on a micro glass ball which only has a small top partabove the gel surface (and the part of the glass ball below the gelsurface is embedded in the gel), and this small top part is less thanhalf of the entire ball. Cell 4 wrapped over this small top part of theglass ball, and further spread on the gel surface. The differentconfigurations represented by Cells 1-4 shown in FIG. 10 should haveincluded the possible key features of a cell wrapping over a micro glassball embedded on the surface of a PA gel. The protocol to prepare themicro glass ball embedded PA gels was described by the authors earlier(Lee and Yang, 2012), and the Young's modulus of the PA gel wasdetermined by the protocol of Wang and Pelham on the PA gel preparation(Wang and Pelham, 1998).

FIGS. 11-13 show the phase-contrast images of the NIH-3T3 fibroblastsgrowing on the micro glass ball embedded PA gels with Young's moduli of75 kPa, 10 kPa, and 1 kPa, respectively. It can be seen that some cells,indicated by the red arrows, wrapped over the micro glass balls andreached the gel surfaces, and further spread on the gel surfaces.Because of the imaging nature of the phase-contrast images and becausethe PA gels are transparent, based on a phase-contrast image we cannotdetermine the part of an embedded micro glass ball that is above the gelsurface and the part of the embedded ball that is below the gel surface.But this does not influence the authors to achieve the objective of thisresearch, to identify the effect of wrapping over a ball on thespreading morphology of a cell, which can be accomplished by analyzingthe obtained phase-contrast images. Irrespective of the differentdiameters of the micro glass balls, different elasticities (i.e.,different Young's moduli) of the PA gels, and different relativelocations of the micro glass balls with respect to the geometric centersof the fibroblasts, the spreading morphologies of the fibroblastswrapping over the micro glass balls in FIGS. 11-13 showed a commoncharacteristic: the outlines or boundaries of these fibroblasts wereroughly circular and smooth, and had no obvious angles, corners, andstraight edges. This roughly-circular and smooth characteristic of theoutlines or boundaries of these fibroblasts indicated that, thesefibroblasts were in isotropic-spreading, and for each of thesefibroblasts the extent of the cell spreading in every direction isroughly the same from the geometric center of the fibroblast.

Because of the geometrically-isotropic nature of the surface of a ball,the isotropic-spreading cell morphologies observed here were formed bywrapping over the micro glass balls, and these cells naturallyisotropically spread over the balls and further naturally spread on theadjacent gel surfaces. Therefore, the cell isotropic-spreading observedhere is cell natural isotropic-spreading, and this is in contrast to thecell isotropic-spreading observed by culturing cells on the geometricpatterns or chemical patterns to control or restrict the spreading ofthe cells. The readers can appreciate the characteristics and uniquenessof the cell natural isotropic-spreading observed here by recalling theirregular and non-uniform nature of the normal cell natural spreadingobserved in the culture dishes, on the flat glass slides (Alberts etal., 2015; ATCC, VA; Life Technologies Corp., NY), on the flat gels (Loet al., 2000; Discher et al., 2005; Engler et al., 2006), on the glassballs but without wrapping over the balls (Lee and Yang, 2012), on theglass fibers (Lee and Yang, 2012; Dunn and Heath, 1976), and on the PLGAmicrofibers (Hwang et al., 2009), where the extent of the cell spreadingin each direction and the resulting cell outline or boundary wererandom, and the cell spreading morphologies had sharp angles, corners,and straight edges. In summary, FIGS. 11-13 showed that wrapping over aball realizes cell natural isotropic-spreading. The rough quantitativeestimations of the cell spread areas and their comparisons of thefibroblasts (shown in FIGS. 11-13) wrapping over the micro glass ballsare presented in the following.

Example 3 Estimating the Spread Area of a Cell that Wrapping Over a Ball

The spread area of a cell that wrapped over a ball and further spread onthe adjacent gel surface is roughly estimated as the spread area of thecell on the ball plus the spread area of the cell on the gel surface.The spread area of the cell on the ball is roughly estimated as πD²_(Ball)/2, i.e., the surface area of the top half of the ball, whereD_(Ball) is the diameter of the ball. According to the configurations ofthe Cells 1-4 in FIG. 10, this estimation of the spread area of the cellon the ball, πD² _(Ball)/2, is the upper bound of the spread area of thecell on the ball, and as described in the above for FIG. 10, it is anaccurate estimation for the Cells 1-3, but it is an overestimate for theCell 4 since the surface area of the ball covered by the Cell 4 issmaller than half of the ball. The spread area of the cell on the gelsurface is roughly estimated as the projected area of the cell onto theflat gel surface minus πD² _(Ball)/4, i.e., minus the area of thediametrical circle of the ball. Again obviously, this estimation of thespread area of the cell on the gel surface is an accurate estimation forthe Cells 1-3, but is an underestimate for the Cell 4. The estimatedtotal spread area of a cell, the spread area of the cell on the ballplus the spread area of the cell on the gel surface, is an accurateestimation for the Cells 1 and 2, but is an underestimate for the Cell 3since the spread area of the cell between the part of the cell thatattached to the ball and the part of the cell that attached to the gelsurface, i.e., the area of the vertical part of the cell morphologywhich is cylindrical and equal to πD_(Ball)h where h is the distancebetween the part of the cell that attached to the ball and the part ofthe cell that attached to the gel surface, is not included. For the Cell4, this estimated total spread area of the cell is an overestimatebecause the overestimate in the estimation of the spread area of thecell on the ball is greater than the underestimate in the estimation ofthe spread area of the cell on the gel surface.

As mentioned in the above, based on a phase-contrast image shown inFIGS. 11-13, one cannot determine the relative height between theembedded micro glass ball and the gel surface. However, the followingthree reasons support the assumption that the fibroblasts wrapping overthe micro glass balls shown in FIGS. 11-13 initially belonged to theconfigurations represented by Cells 1-3 shown in FIG. 10, i.e., abouthalf or more than half of each of the embedded micro glass balls wasabove the corresponding gel surface, and if a fibroblast wrapping over amicro glass ball shown in FIGS. 11-13 belonged to the configurationrepresented by Cell 3 shown in FIG. 10, the vertical distance from thegeometric center of the micro glass ball to the gel surface should bemuch smaller than the radius of the micro glass ball, i.e., thegeometric center of the micro glass ball was a little above the gelsurface or a little smaller than half of the micro glass ball was underthe gel surface. First, as shown in the scanning electron microscope(SEM) image (not shown here) of a micro glass ball embedded PA gelpublished by the authors earlier (Lee and Yang, 2012), about half ormore than half of each of the embedded micro glass balls was above thegel surface. Secondly, the micro glass balls used to make the microglass ball embedded PA gels were not solid balls, they were empty balls,or they were made of glass shells. Thus they were lighter than the PAsolutions, and they were floating on the top of the PA solutions. Theauthors had to use coverslips to press the micro glass balls down intothe PA solutions to make the micro glass ball embedded PA gels. Duringand after the polymerization process of the PA solutions, because of thelighter situation, the micro glass balls were believed to move graduallyupward in the polymerizing PA solutions and polymerized PA gels to reacha force equilibrium in the vertical direction. When the prepared microglass ball embedded PA gels were used for cell culturing, theexperiences of the authors told the authors that about half or more thanhalf of each of the embedded micro glass balls on which there werefibroblasts growing should be above the gel surface and if it was thecase that more than half of an embedded micro glass ball on which therewere fibroblasts growing was above the gel surface, the geometric centerof the micro glass ball was just a little above the gel surface.Thirdly, for an embedded micro glass ball to survive (i.e., not detachfrom the gel during) the entire handling (including transportation,rinsing, and adding the cell culture media) process, for an embeddedmicro glass ball to provide a stable substrate for a cell to adhere andspread, and for an embedded micro glass ball to survive the entire cellgrowing process until the imaging time, about half or a little smallerthan half of the micro glass ball need to be under the gel surface.

The stabilized configurations (or can be called the final configurationsin contrast to the initial configurations mentioned at the beginning oflast paragraph) of the fibroblasts wrapping over the micro glass ballsshown in FIGS. 11-13 should only belong to the configurationsrepresented by Cells 1 and 2 shown in FIG. 10, i.e., about half of eachof the embedded micro glass balls was above the corresponding gelsurface. This is because the vertical adhesion/pulling forces betweenthe cell and the gel surface will gradually press the micro glass balldown a little and pull the gel surface up a little to adjust thevertical relative position between the cell and the gel surface to reachan optimum mechanobiologically-comfortable position/morphology of thecell, and Cell 3 in FIG. 10 has a vertically-stretched (with a height ofh) part and was not believed to be a mechanobiologically-comfortableposition and a cell should prefer the position of Cell 1 or 2 more thanthe position of Cell 3 in FIG. 10. Due to the relatively very largevolume of the gel material surrounding the embedded micro glass ball,the vertical deformation induced by the vertical adhesion/pulling forcesbetween the cell and the gel surface will not significantly change theplanar nature of the gel surface. One additional justification of theabove statement, the stabilized configurations of the fibroblastswrapping over the micro glass balls shown in FIGS. 11-13 should onlybelong to the configurations represented by Cells 1 and 2 in FIG. 10,was that, the part of the morphology of each of these fibroblasts on thecorresponding PA gel surface indicated that the fibroblast wrapped overapproximately the top half of the micro glass ball and there was noobvious vertically-stretched part, otherwise if the fibroblasts had theconfigurations represented by Cells 3 and 4 in FIG. 10, the fibroblastswould have not spread such uniformly around the diameters of the balls.Therefore, for the fibroblasts wrapping over the micro glass balls shownin FIGS. 11-13, the method introduced in the first paragraph of thissection should give reasonably-accurate estimations for the spread areaof a fibroblast on the ball, for the spread area of this cell on the gelsurface, and for the total spread area of this cell.

In FIG. 11, the fibroblast wrapped over a micro glass ball (embedded ina PA gel with a Young's modulus of 75 kPa) with a diameter of 33.8 μm,and the image was taken after 48 h in culture. The spread area of thiscell on the ball was estimated as 1794.5 μm² and the spread area of thiscell on the gel surface was estimated as 421.4 μm². The total spreadarea of this cell was then estimated as 2215.9 μm². The projected areaof this cell onto the flat gel surface was measured as 1318.6 μm². Inthe below, the projected area of a cell onto a flat gel surface iscalled the cell projected area or the projected area of this cell. Sinceas stated in the above, the morphologies of the observed fibroblastswrapping over the micro glass balls were approximately circular, thediameter of such a fibroblast was estimated according to the followingareal relation, cell projected area=πD² _(cell)/4, where Dun was theestimated diameter of this fibroblast. The diameter of the fibroblastwrapping over the micro glass ball in FIG. 11 was then estimated as 41.0μm, which was 1.213 times the diameter of the micro glass ball, i.e.,the further spreading of this cell on the gel surface in the radialdirection (after this cell wrapped over the micro glass ball) wasapproximately 21.3% of the radius of the micro glass ball.

In FIG. 12, there are two fibroblasts wrapped over the two micro glassballs (embedded in a PA gel with a Young's modulus of 10 kPa). The upperfibroblast in FIG. 12 (B) wrapped over a micro glass ball with adiameter of 24.4 μm. The spread area on the ball, the spread area on thegel surface, and the total spread area of this cell were estimated as935.2, 303.7, and 1238.9 μm², respectively. The projected area of thiscell was measured as 771.3 μm², and the diameter of this cell wasestimated as 31.3 μm which was 1.283 times the diameter of the microglass ball, i.e., the further spreading of this cell on the gel surfacein the radial direction was approximately 28.3% of the radius of themicro glass ball. The lower fibroblast in FIG. 12 (B) wrapped over amicro glass ball with a diameter of 25.2 μm. The spread area on theball, the spread area on the gel surface, and the total spread area ofthis cell were estimated as 997.5, 416.5, and 1414.0 μm², respectively.The projected area of this cell was measured as 915.2 μm², and thediameter of this cell was estimated as 34.1 μm which was 1.353 times thediameter of the micro glass ball, i.e., the further spreading of thiscell on the gel surface in the radial direction was approximately 35.3%of the radius of the micro glass ball. Since the image shown in FIG. 12was taken after 96 h in culture, these two cells (the just mentionedupper fibroblast and lower fibroblast in FIG. 12 (B)) may be the twodaughter cells of a cell division. Compared with the situation of thefibroblast wrapped over the micro glass ball in FIG. 11, the two microglass balls in FIG. 12 were much smaller, and then the cell spread areason the micro glass balls of the two fibroblasts in FIG. 12 were muchsmaller than that of the fibroblast in FIG. 11. But the relative (withrespect to the radius of the micro glass ball) further spreading in theradial direction of these two fibroblasts on the gel surface weresignificantly larger than that of the fibroblast in FIG. 11 even thoughthe PA gel in FIG. 12 was much softer than the PA gel in FIG. 11, whichindicated that these two fibroblasts tended to spread more on the gelsurface because they spread less on the micro glass balls. Thisobservation agreed well with the theoretical reasoning presented in theabove in the description of FIG. 10 for the configurations of Cells 1and 2.

In FIG. 13, the micro glass balls were embedded in a PA gel with aYoung's modulus of 1 kPa. The images shown in FIGS. 13 (A) and (B) weretaken after 48 hours in culture, and the fibroblast in FIG. 13 (B)wrapped over a micro glass ball with a diameter of 26.5 μm. The imagesshown in FIGS. 13 (C) and (D) were taken after 96 hours in culture, andin FIG. 13 (D) the two fibroblasts wrapped over the micro glass ball maybe the two daughter cells of a cell division. In FIG. 13 (D) the microglass ball has a diameter of 15.2 μm, which was much smaller than thatof the micro glass ball wrapped over by the fibroblast in FIG. 13 (B).Therefore, the situations that FIG. 13 intended to observe combined thesituations that were observed in FIGS. 11 and 12, but here in FIG. 13the micro glass balls in both FIG. 13 (A) and (B) and FIGS. 13 (C) and(D) were embedded in a PA gel with a Young's modulus of 1 kPa, whereasin FIGS. 11 and 12 the micro glass balls were embedded in PA gels withYoung's moduli of 75 and 10 kPa, respectively. For the fibroblast inFIG. 13 (B) wrapped over the micro glass ball, the spread area on theball, the spread area on the gel surface, and the total spread area ofthis cell were estimated as 1103.1, 190.3, and 1293.4 μm², respectively.The projected area of this cell was measured as 741.8 μm², and thediameter of this cell was estimated as 30.7 μm which was 1.158 times thediameter of the micro glass ball, i.e., the further spreading of thiscell on the gel surface in the radial direction was approximately 15.8%of the radius of the micro glass ball.

For the upper one of the two fibroblasts wrapped over the micro glassball in FIG. 13 (D), the spread area on the ball, the spread area on thegel surface, and the total spread area of this cell were estimated as362.9, 160.6, and 523.5 μm², respectively. The projected area of thiscell was measured as 342.0 μm², and the diameter of this cell wasestimated as 20.9 μm which was 1.375 times the diameter of the microglass ball, i.e., the further spreading of this cell on the gel surfacein the radial direction was approximately 37.5% of the radius of themicro glass ball. For the lower one of the two fibroblasts wrapped overthe micro glass ball in FIG. 13 (D), the spread area on the ball, thespread area on the gel surface, and the total spread area of this cellwere estimated as 362.9, 121.8, and 484.7 μm², respectively. Theprojected area of this cell was measured as 303.2 μm², and the diameterof this cell was estimated as 19.6 μm which was 1.289 times the diameterof the micro glass ball, i.e., the further spreading of this cell on thegel surface in the radial direction was approximately 28.9% of theradius of the micro glass ball. Compared with the situation in FIG. 13(B), the micro glass ball in FIG. 13 (D) was much smaller, and then thecell spread areas on the micro glass ball of the two fibroblasts in FIG.13 (D) were much smaller than that of the fibroblast in FIG. 13 (B). Butthe relative further spreading in the radial direction of these twofibroblasts on the gel surface were significantly larger than that ofthe fibroblast in FIG. 13 (B), which indicated that these twofibroblasts tended to spread more on the gel surface because they spreadless on the micro glass ball. This observation again agreed well withthe theoretical reasoning presented in the above in the description ofFIG. 10 for the configurations of Cells 1 and 2. Moreover, the relativefurther spreading in the radial direction of the fibroblast in FIG. 13(B) on the gel surface was significantly smaller than those of thefibroblasts in FIGS. 11 and 12, and this may be due to the fact that thePA gel in FIG. 13 was much softer than the PA gels in FIGS. 11 and 12.But since the micro glass ball in FIG. 13 (D) was too small, the cellspread areas on the micro glass ball of the two fibroblasts (the justmentioned upper fibroblast and lower fibroblast in FIG. 13 (D)) in FIG.13 (D) were also too small. The relative further spreadings in theradial direction of these two fibroblasts on the gel surface were stillsimilar to those of the two fibroblasts in FIG. 12 (B), which againsupported the above-mentioned notion that these two fibroblasts tendedto spread more on the gel surface because they spread less on the microglass ball.

Example 4 Mechanism for the Observed Cell Natural Isotropic-Spreading

The attachment rate and spreading morphology of the NIH-3T3 fibroblastsare sensitive to the diameters of their substrate micro glass balls,i.e., are sensitive to the curvatures of their substrates (Lee and Yang,2012). For the fibroblasts growing on the micro glass balls withdiameters of 500 μm and below, round shapes were the dominant cellmorphology, and some cells made one or two long and narrow lamellipodiawhile the cell body was still round. These indicated that the largecurvatures of the surfaces of small micro glass balls, such as the microglass balls with diameters of 500 μm and below, inhibit the formation oflong stress fibers inside a cell.

FIG. 14 schematically shows the mechanism or process to form theobserved cell natural isotropic-spreading here, i.e., the speculatedprocess for a cell to wrap over a micro glass ball. In FIG. 14 (A), acell attached to a micro ball and started to spread. Because of thelarge surface curvature of the micro ball, long stress fibers inside thecell could not be formed, and then the cell made two long and narrowlamellipodia in two opposite or symmetric and energetically-favorabledirections while the cell body was still round (FIG. 14 (B)). Thesymmetric distribution of these two long and narrow lamellipodia withrespect to the cell body was to ensure the statical equilibrium of thecell. Because of the small size of the micro ball, the two long andnarrow lamellipodia could extend to reach to the surface of the gel, andformed focal adhesions with the gel surface (FIG. 14 (C)). The adhesionforces provided by these two adhesion sites, formed between the two longand narrow lamellipodia and the gel surface, made the cell morestretched and spreading morphology more stable. This more stabilizedcell morphology provided the cell with more freedom to spread, and thenthe other two opposite or symmetric and energetically-favorable sites onthe periphery of the round part of the cell body started to extend tomake long and narrow lamellipodia, and these two newly-made long andnarrow lamellipodia could also extend to reach to the surface of thegel, and formed focal adhesions with the gel surface (FIG. 14 (D)). Thisprocess continued at the other sites on the periphery of the round partof the cell body (FIG. 14 (E)) until the entire cell periphery extendedand adhered to the gel surface (FIG. 14 (F)). The cell periphery furthernaturally spread on the adjacent gel surface and this further spreadingwas roughly-isotropic because of the lack of long stress fibers insidethe cell. Therefore, in short, the underlying reason for the cellnatural isotropic-spreading observed here was speculated as follows: Thelarge curvature of the surface of a ball inhibits the formation of longstress fibers inside a cell, and the adhesion forces between the celland the adjacent gel surface pull the cell to spread to wrap over theball and further spread on the adjacent gel surface roughly in the sameamount in every direction.

Example 5 Micro Glass Ball Embedded PA Gel Experimental Platforms

A class of PA gels embedded with micro glass balls having diameters ofmixed 5-100 μm, mixed 50-300 μm, 500 μm, 750 μm, 900 μm, 1.1 mm, 2 mm, 3mm, and 4 mm were prepared by using the protocol described in Materialsand Methods. FIG. 15 (a) shows the schematic drawing of a micro glassball embedded PA gel experimental platform for studying cellmechanobiological responses to substrate curvatures. Since this platformis non-flat, it provides a 3D micromechanical environment for cellculturing. Also, since the surface curvatures of the non-flat glassballs are known or defined, we say this 3D micromechanical environmentis curvature-defined. In this platform, the polymerized PA gel is to fixthe glass balls at certain locations on and to prevent any rolling anddetaching of the glass balls from the gel surface. FIGS. 15 (b) and (c)show bright-field optical pictures of two PA gel experimental platformswith embedded glass balls having diameters of 500 μm and 2 mm,respectively.

Example 6 Effects of Substrate Curvatures on the Spreading of NIH-3T3Fibroblasts

The surface curvature of a substrate is the reciprocal of the radius ofthe substrate. Among the used diameters of glass balls, it was foundthat the minimum diameter of a glass ball on which a NIH-3T3 fibroblastcan attach and spread without wrapping over the ball was 58 μm. Afibroblast wrapping over a ball means this fibroblast covered the entireupper exposed portion of the embedded ball in a PA gel and furtherspread on the adjacent gel surface. The cell attachment rate is definedas the ratio between the number of the attached and spread cells on theglass balls and the number of the seeded cells in a cell culture dish.The cell attachment rates were not quantitatively measured, and the cellattachment rates were difficult to measure because the number of theattached and spread cells on the glass balls was difficult to count. Asshown in FIGS. 15 (b) and (c), the embedded glass balls were packed onthe surfaces of the PA gels. Since we seeded the same number of cellsinto each cell culture dish, we used the chance of finding an attachedand spread cell on a glass ball as a qualitative measure of the cellattachment rate on the glass balls with a same diameter and packed onthe surface of a PA gel, and then we qualitatively found that the cellattachment rate of the fibroblasts decreased with the decrease of thesubstrate ball diameter.

FIG. 16 shows the effects of the substrate curvatures on the spreadingmorphologies of the NIH-3T3 fibroblasts growing on the micro glass ballswith various diameters. The following morphological observations on thefibroblasts growing on the micro glass balls with various diameters werereported (Lee and Yang, 2012; incorporated herein by reference inentirety). But in FIG. 2 of Lee and Yang, the phase-contrast images ofthe fibroblasts growing on the glass balls were taken by using a 40×objective to show the morphology of a single cell, while here in FIG.16, the phase-contrast images were taken by using a 10× objective tocover much larger surface areas of the glass balls to show themorphologies of multiple cells growing on a glass ball. Therefore, onecan learn the following information from FIG. 16 here, the zoom-out viewof a cell growing on a ball surface and the morphologies of differentcells growing on the same ball surface. The present disclosure describesthe effects of the substrate curvatures on the spreading morphologies ofthe fibroblasts.

In the experiments, it was observed that after 24 hours in culture, theNIH-3T3 fibroblasts started to divide and the two daughters of anoriginal cell were connected to each other. Therefore, to image singlefibroblasts, 24 hours in culture was chosen as the fibroblasts' imagingtime. After 24 hours in culture, the fibroblasts growing on the flatglass plate (FIG. 16 (a)) were well-spread, and the spreadingmorphologies of these fibroblasts were almost indistinguishable fromthose of the fibroblasts growing on the 2 mm-diameter glass ball (forbrevity, the words “growing”, “diameter”, and “glass” in this statementwill be omitted in the below in the same or similar statements unlessthis omission may induce unclarity, e.g., this statement will read as“fibroblasts on the 2 mm-ball” and “the flat glass plate(s)” will readas “the flat plate(s)” in the below) (FIG. 16 (b)). Both the fibroblastson the flat plate and the fibroblasts on the 2 mm-ball had two or threelamellipodia for active migration. Although both the fibroblasts on the2 mm ball and the fibroblasts on the flat plate had the similarmorphologies and behaviors, the fibroblasts on the 2 mm-ball wereslightly less spread than the fibroblasts on the flat plate. This meansthat these cells can sense the small substrate curvature of a largesubstrate radius or diameter, such as the small surface curvature of the2 mm-diameter substrate glass balls used herein.

Compared with the fibroblasts on the flat plate and 2 mm-ball, thefibroblasts on the 1.1 mm-(FIG. 16 (c)), 900 μm-FIG. 16 (d)), and 750μm-(FIG. 16 (e)) balls were less spread and had the similar morphologieswhich are different from those of the fibroblasts on the flat plate and2 mm-ball. While some of the fibroblasts on the 1.1 mm-, 900 μm-, and750 μm-balls had the round shapes with two short and wide lamellipodiaafter 24 hours in culture, the majority of the fibroblasts had the morespread shapes.

The fibroblasts on the balls with diameters of 500 μm and below (FIGS.16 (f), (g), and (h)) had the very different cell shapes, compared withthose on the larger balls. For these cells, the round shapes were thedominant cell morphology, and some of the cells made one or two long andnarrow lamellipodia while the cell body was still round. As shown inFIGS. 16 (g) and (h), the morphologies of the fibroblasts on the 147 μm-and 58 μm-balls closely resembled the morphology of the fibroblast onthe 500 μm-ball (FIG. 16 (f)), and all the three fibroblasts were roundwith one or two lamellipodia. It was also observed that the fibroblastson the balls with diameters of 500 μm and below did not spread andmigrate actively, and they grew minimally and remained round after 48hours in culture.

For the cells growing on the balls, the cell dimensions, including thecell lengths and widths, and the cell spread areas are all importantquantitative information to reveal the effects of the substratecurvatures on cell shape and function. Then, the cell lengths, cellwidths, and cell spread areas were measured for a number ofrandomly-selected fibroblasts growing on the flat plates and on theballs. For the fibroblasts growing on the flat plates, 10 cells weremeasured, and for the fibroblasts growing on the 2 mm-, 1.1 mm-, 900μm-, 750 μm-, and 500 μm-balls, 10 cells were measured for each balldiameter. For the fibroblasts growing on the balls with diameters of 300μm and below, since the cell attachment rates of these balls were muchlower than those of the balls with diameters of 500 μm and above, 35cells in total were measured, including the cell on a ball with adiameter of 58 μm (as mentioned in the above, 58 μm was the observedminimum diameter of a glass ball on which a fibroblast can attach andspread without wrapping over the ball). Then the total number of themeasured fibroblasts is n_(fibroblasts)=10×(1+5)+35=95.

FIG. 17 shows the measurement results of the cell dimensions of thesemeasured fibroblasts. For the fibroblasts on the balls with diameters of500 μm and above including the case of the flat plates (same in thebelow unless otherwise stated), the results shown are mean±SD for eachball diameter. For the fibroblasts on the balls with diameters of 300 μmand below, the results shown are for each individual cell. FIG. 18 showsthe measurement results of the cell spread areas of these measuredfibroblasts. The statistical analysis results of ANOVA with Tukey's posthoc test were added in FIG. 18. In contrast to FIG. 17, in FIG. 18, forthe fibroblasts on the balls with diameters of 500 μm and above, besidesthe mean±SD result for each ball diameter, the spread area of eachindividual fibroblast is also shown. The measurement results andstatistical analyses of these fibroblasts is shown in Table 1.

TABLE 1 Cell length, width, aspect ratio, and spread areas of NIH- 3T3fibroblasts grown on balls of various diameters. Ball diameter Flat 2 mm1.1 mm 900 μm Cell mean ± SD 110.1 ± 26.9  112.9 ± 40.7  117.8 ± 48.0 78.8 ± 14.3 length maximum 177.1 197.4 230.8 98.3 (μm) minimum 84.6 64.864.0 54.5 Cell mean ± SD 25.2 ± 23.4 25.5 ± 10.6 17.0 ± 2.7  16.0 ± 2.3 width maximum 86.7 47.7 20.8 19.2 (μm) minimum 13.5 15.5 13.4 12.8 Cellmean ± SD 0.248 ± 0.245 0.275 ± 0.204 0.165 ± 0.072 0.213 ± 0.069 aspectmaximum 0.879 0.717 0.326 0.337 ratio minimum 0.062 0.105 0.098 0.133Cell mean ± SD 1592.3 ± 751.9  1368.4 ± 678.1  996.7 ± 322.0 660.1 ±113.4 spread maximum 3166.7 2347.3 1710.1 771.1 Area minimum 816.2 679.9559.7 424.2 (μm²) Ball diameter 750 μm 500 μm 300 μm and below Cell mean± SD 76.0 ± 18.0 94.2 ± 44.5 59.1 ± 28.9 length maximum 105.4 164.5116.8 (on a 249.5 μm-ball) (μm) minimum 55.6 42.6 12.4 (on a 70.6μm-ball) Cell mean ± SD 14.7 ± 2.9  16.1 ± 3.0  15.2 ± 2.9  widthmaximum 20.1 20.6 22.4 (on a 91.2 μm-ball) (μm) minimum 11.3 12.5 10.0(on a 74.1 μm-ball) Cell mean ± SD 0.203 ± 0.061 0.208 ± 0.102 0.357 ±0.250 aspect maximum 0.311 0.424 0.907 (on a 70.6 μm-ball)  ratiominimum 0.121 0.089 0.130 (on a 249.5 μm-ball) Cell mean ± SD 634.5 ±212.5 549.2 ± 238.4 429.0 ± 124.9 spread maximum 1059.5 948.5 719.7 (ona 227.8 μm-ball) Area minimum 379.6 257.5 208.7 (on a 63.0 μm-ball) (μm²)

In FIG. 17, for the cell lengths, the overall trend is, starting fromthe case of the flat plates, the mean length of the fibroblasts did notdecrease significantly with the decrease of the substrate ball diameterdown to 300 μm when the monotonic decrease of the cell length started.For the fibroblasts on the balls with diameters of 300 μm and below, incontrast to the lengths of the fibroblasts, the widths of thefibroblasts did not distribute widely.

For the fibroblasts on the 2 mm-balls and the fibroblasts on the flatplates, except for the large difference in the SD values of their cellwidths, their mean cell widths were similar, which is supported by theirsimilar well-spread cell morphologies with two or three lamellipodia asshown in FIGS. 16 (a) and (b). With the decrease of the ball diameterfrom 2 mm to 1.1 mm, both the mean cell width and the corresponding SDvalue decreased abruptly, which also agreed with the significant changesin the cell morphology (FIGS. 16 (b) and (c)). For all the fibroblastson the balls with diameters of 1.1 mm and below, the cell widths weresimilar and did not vary significantly, i.e., there was no significantfurther decrease in the cell width with the decrease in the balldiameter, and the mean cell width of all these cells was 15.3 μm. Also,as shown in FIG. 16 (c-h), the spindle-shape was the dominant cellmorphology of all these fibroblasts. Since the cell nucleus must beenclosed in the cell body, the minimum width of a spindle-shaped cell isdecided by the minimum width of the cell nucleus, which explains why thecell widths of all the fibroblasts on the balls with diameters of 1.1 mmand below were similar and provides a measurement for the minimum widthof the cell nucleus of an attached and spread cell.

The dramatically-wide distribution of the cell aspect ratios of thefibroblasts on the balls with diameters of 300 μm and below (FIG. 17) isdue to the morphology, round shape with one or two long and narrowlamellipodia, of some of these fibroblasts.

In FIG. 18, for the fibroblasts on the balls with diameters of 500 μmand above, the mean cell spread area decreased monotonically with thedecrease of the ball diameter, from the flat plates to the larger ballsto the smaller balls, and decreased from 1592.3 μm² to 549.2 μm². Theoverall trend of the cell spread areas of the fibroblasts on the ballswith diameters of 300 μm and below is a monotonic decrease with thedecrease of the ball diameter, which is consistent with the overalltrends of the measurement results of the cell dimensions of thesefibroblasts, a monotonic decrease in the cell length and aninsignificant variation in the cell width (FIG. 17).

As labeled in FIG. 18, according to the variation of the measured spreadareas of the fibroblasts on the balls with diameters of 300 μm and belowand the mean spread areas of the fibroblasts on the balls with diametersof 500 μm and above versus the ball diameter, all the measured cellspread areas were divided into the following three regions, Region 1,Region 2, and Region 3 (Lee and Yang, 2012). Region 1 includes thespread areas of the fibroblasts on the balls with diameters of 300 μmand below and these cell spread areas were fitted by a linear relation,y_(linear)=1.199x+241.3. Region 2 includes the spread areas of thefibroblasts on the balls with diameters of 500 μm, 750 μm, and 900 μm,and the corresponding three mean spread areas were fitted also by alinear relation, y_(linear)=0.284x+411.2. The slope of this linearrelation was 23.7% of the slope of the fitting linear relation ofRegion 1. Region 3 includes the spread areas of the fibroblasts on theballs with diameters of 1.1 mm and 2 mm and on the flat plates, and thecorresponding three mean spread areas were fitted by an exponentialrelation, y_(exponential)=1838−1715e^((−x/1544)). Because the radius ofcurvature of the flat plates is infinity, while the diameters of 1.1 mmand 2 mm are finite numbers, an exponential relation is the suitablerelation to curve-fit the asymptotic trend of the mean spread areas ofthe fibroblasts on the balls with diameters from 1.1 mm to 2 mm toinfinity (which is the case of the flat plates). The slope between thetwo data points of the mean spread areas for the fibroblasts on 1.1 mm-and 2 mm-balls was 0.413, which was 34.4% of the slope of the fittinglinear relation of Region 1. Therefore, Region 1's fitting linearrelation had the largest slope compared with those of Regions 2 and 3.Also, note that, from the 900 μm-balls to the 1.1 mm-balls, there was a51.0% sudden rise in the mean cell spread area of the fibroblasts. Fromthe above linear fitting analysis, we concluded that, overall, the cellspread area of the fibroblasts increased with the increase of the balldiameter with three different slopes in the three distinct regionsdepending on the ball diameters.

Example 7 Effects of the Substrate Curvatures on the SpreadingMorphologies of the hMSCs

The surface curvature of a substrate is the reciprocal of the radius ofthe substrate.

We defined the cell attachment rate as the ratio between the number ofthe attached and spread cells on the glass balls and the number of theseeded cells in a cell culture dish. We did not quantitatively measurethe cell attachment rates in this study, and the cell attachment rateswere difficult to measure because the number of the attached and spreadcells on the glass balls was difficult to count. As shown in FIGS. 15(b) and (c), the embedded glass balls were packed on the surfaces of thePA gels. Since we seeded the same number of cells into each cell culturedish, we used the chance of finding an attached and spread cell on aglass ball as a qualitative measure of the cell attachment rate on theglass balls with a same diameter and packed on the surface of a PA gel.

Among the used diameters of glass balls, we found that the minimumdiameter of a glass ball on which an hMSC can attach and spread was 500μm. We qualitatively found that the cell attachment rate of the hMSCsdecreased with the decrease of the substrate ball diameter.

FIG. 19 shows the effects of the substrate curvatures on the spreadingmorphologies of the hMSCs growing on the glass balls with variousdiameters. Since the hMSCs spread much slower than the NIH-3T3fibroblasts, the spreading morphologies of the hMSCs were imaged after96 hours in culture when the hMSCs started to divide, instead of theNIH-3T3 fibroblasts' imaging time, after 24 hours in culture (when thefibroblasts started to divide), which we used before (Lee and Yang,2012).

In the following, for brevity, the words “growing”, “glass”, and“diameter” will be omitted unless this omission may induce unclarity.For examples, “hMSCs growing on the flat glass plate” will read as“hMSCs on the flat plate” and “hMSCs growing on the 2 mm-diameter glassball” will read as “hMSCs on the 2 mm-ball”.

After 96 hours in culture, the hMSCs on the flat plates were well-spread(FIG. 19 (a)), the hMSCs had at least two or three long or short narrowor wide lamellipodia, some of the hMSCs had five or more lamellipodiafor active migration, some of the hMSCs were connected to each other bylong lamellipodia and cell division began to occur at this time. Incontrast to the hMSCs on the flat plates, the hMSCs on the 4 mm-, 3 mm-,2 mm-, 1.1 mm-, 900 μm-, 750 μm-, and 500 μm-balls were much lessspread, and regardless of the ball diameters, the majority of hMSCs onthe balls had the same morphology, spindle-shape with two long or shortnarrow lamellipodia (FIG. 19 (b)-(h)). For each ball diameter includingthe case of the flat plates (same in the below unless otherwise stated),30 randomly-selected hMSCs were observed and measured. Table 2 shows thetotal count of the hMSCs having the number of lamellipodia for each balldiameter. For the 30 hMSCs on the flat plates, the number oflamellipodia of each cell was random. Among the observed numbers oflamellipodia that an hMSC could have, three lamellipodia was the numberof lamelipodia that had the maximum number of cells, which was 11. Therewere seven cells each of which had only two lamellipodia, which was theminimum number of lamellipodia observed in this study for an hMSC on aflat plate or a ball. There were two cells each of which had sevenlamellipodia, which was the maximum number of lamellipodia observed inthis study for an hMSC on a flat plate or a ball. For the 30 hMSCs onthe balls with each of the diameters, there were only a small portion,from 2/30 (≈6.7%) to 7/30 (≈23.3%), of the cells having more than twolamellipodia. For all the 180 hMSCs on the balls having diameters of 3mm and below, there were no any cells having more than threelamellipodia. For the 30 hMSCs on the 4 mm-balls, there was only onecell having four lamellipodia, and there were not any cells having morethan four lamellipodia.

TABLE 2 Number of the hMSCs having the number of lamellipodia. The totalnumber of the hMSCs measured for each ball diameter was 30. The “Mean ±SD” is the mean ± SD of the numbers of lamellipodia of the hMSCs growingon the balls of each diameter. Number of the hMSCs, growing on the ballsof each diameter, having the Number of number of lamellipodialamellipodia Flat 4 mm 3 mm 2 mm 1.1 mm 900 μm 750 μm 500 μm 1 0 0 0 0 00 0 0 2 7 23 24 24 27 28 26 26 3 11 6 6 6 3 2 4 4 4 8 1 0 0 0 0 0 0 5 20 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 2 0 0 0 0 0 0 0 Mean ± SD 3.4 ± 1.32.3 ± 0.5 2.2 ± 0.4 2.2 ± 0.4 2.1 ± 0.3 2.1 ± 0.3 2.1 ± 0.3 2.1 ± 0.3

The fact that, no hMSCs were found to attach and spread on the ballswith diameters of 300 μm and below, indicates that it is difficult foran hMSC to adhere to the surfaces of glass balls with small radii orlarge curvatures, such as the radii at or below 150 μm.

Example 8 Cell Dimensions of the Measured hMSCs

For the cells growing on the balls, the cell dimensions, including thecell lengths and widths, and the cell spread areas are all importantquantitative information to reveal the effects of the substratecurvatures on cell shape and function. The cell lengths and widths, andthe cell spread areas were measured for the above-mentionedrandomly-selected 30 hMSCs on the flat plates and 30 hMSCs for each ofthe above-mentioned seven ball diameters. FIG. 20 shows the measurementresults of the cell dimensions of these measured hMSCs. FIG. 21 showsthe measurement results of the cell spread areas of these measuredhMSCs. Supplementary to FIGS. 20 and 21, Table 3 also lists thenumerical results of the statistical analysis on these measurementresults. In FIG. 20, overall the mean cell length of the hMSCs decreasedmonotonically with the decrease of the substrate ball diameter, and themean cell length varied between 155.5 μm and 408.4 μm. According to thevalues of the mean cell lengths of the hMSCs, the mean cell lengths ofthe hMSCs can be divided into the following three groups. Group 1includes the four mean cell lengths for the hMSCs on the 500 μm-, 750μm-, 900 μm-, and 1.1 mm-balls, and these four mean cell lengths overallalso have the similar values. Group 2 includes the three mean celllengths for the hMSCs on the 2 mm-, 3 mm-, and 4 mm-balls, and thesethree mean cell lengths overall have the similar values. Group 3includes only the mean cell length of the hMSCs on the flat plates. Themean cell lengths of the hMSCs on the 4 mm- and 2 mm-balls was 71.0% and74.5% of that of the hMSCs on the flat plates, respectively, whereas themean cell length of the NIH-3T3 fibroblasts on the 2 mm-balls was verysimilar to that of the fibroblasts on the flat plates (Lee and Yang,2012). This observation indicates that the cell lengths of the hMSCswere much more sensitive than those of the fibroblasts to the smallcurvatures or the large radii of the large substrate glass balls, e.g.,the radii of 2 mm and 1 mm used here.

TABLE 3 Cell length, width, aspect ratio, and spread areas of hMSCsgrown on balls of various diameters. Ball diameter Flat 4 mm 3 mm 2 mmCell mean ± SD 408.4 ± 102.1 289.8 ± 96.1  241.1 ± 103.9 304.4 ± 79.3 length maximum 622.1 584.6 478.2 512.4 (μm) minimum 176.2 167.7 92.8149.4 Cell mean ± SD 35.8 ± 16.9 20.1 ± 8.5  14.3 ± 4.8  14.5 ± 5.3 width maximum 85.2 44.0 29.5 38.0 (μm) minimum 16.8 10.2 9.0 9.1 Cellmean ± SD 0.092 ± 0.043 0.075 ± 0.035 0.074 ± 0.046 0.051 ± 0.025 aspectmaximum 0.181 0.163 0.205 0.157 ratio minimum 0.027 0.026 0.025 0.025Cell mean ± SD 12629.2 ± 4883.7  7133.7 ± 3503.4 6269.3 ± 3024.7 5700.2± 3373.9 spread maximum 22430.4 16336.6 13296.3 17798.6 Area minimum3790.0 2478.6 1683.6 1322.7 (μm²) Ball diameter 1.1 mm 900 μm 750 μm 500μm Cell mean ± SD 155.5 ± 94.8  202.4 ± 108.7 199.8 ± 67.8  177.2 ±71.2  length maximum 527.5 506.0 389.7 341.2 (μm) minimum 50.1 60.3101.2 77.0 Cell mean ± SD 17.7 ± 7.0  18.0 ± 4.5  15.4 ± 6.0  14.5 ±4.4  width maximum 35.5 27.4 42.0 24.7 (μm) minimum 9.6 10.0 8.6 6.8Cell mean ± SD 0.138 ± 0.068 0.122 ± 0.089 0.086 ± 0.047 0.091 ± 0.038aspect maximum 0.286 0.370 0.292 0.196 ratio minimum 0.037 0.041 0.0430.039 Cell mean ± SD 2282.8 ± 2725.6 3068.6 ± 2939.2 2698.2 ± 1879.12043.5 ± 1204.3 spread maximum 13426.9 13220.4 8642.3 5794.8 Areaminimum 463.3 354.2 796.4 721.1 (μm²)

Except the mean cell width of the hMSCs on the flat plates, the meancell widths of the hMSCs on all the balls (with diameters from 500 μm to4 mm) were similar (FIG. 20), and the mean cell width of all the hMSCson the balls with diameters from 500 μm to 4 mm was 16.4 μm. Thissimilarity phenomenon observed here for all the mean cell widths of thehMSCs on the balls can be explained by the same spindle-shape cellmorphology enclosing the cell nucleus, because the minimum width of aspindle-shaped cell is decided by the minimum width of the cell nucleus(FIG. 19 (b)-(h)). The mean cell width of the hMSCs on the flat platesincreased abruptly from 20.1 μm, the mean cell width of the hMSCs on the4 mm-balls, to 35.8 μm. This is consistent with the abrupt morphologychange of most of the hMSCs, from the spindle-shape with two long orshort narrow lamellipodia on the 4 mm-balls to the well-spread shapewith randomly-multiple lamellipodia on the flat plates. The mean cellwidths of the hMSCs on the 4 mm- and 2 mm-balls were 56.1% and 40.5% ofthat of the hMSCs on the flat plates, respectively, whereas the meancell width of the NIH-3T3 fibroblasts on the 2 mm-balls was very similarto that of the fibroblasts on the flat plates (Lee and Yang, 2012). Thisobservation indicates that the cell widths of the hMSCs were also muchmore sensitive than those of the fibroblasts to the small curvatures orthe large radii of the large substrate glass balls, e.g., the radii of 2mm and 1 mm used here.

The mean cell aspect ratio of these hMSCs varied between 0.051 and0.138, which were much lower than those of the NIH-3T3 fibroblasts. Themuch lower mean cell aspect ratios of these hMSCs are due to themorphologies of most of these hMSCs, the spindle-shapes with two long orshort lamellipodia (FIG. 19), whereas the morphologies of thefibroblasts were much more spread (Lee and Yang, 2012).

In FIG. 21, overall, similar to the case of the NIH-3T3 fibroblasts (Leeand Yang, 2012), the mean cell spread area of these hMSCs decreased withthe decrease of the ball diameter, from the flat plates to the largerballs to the smaller balls. All the mean cell spread areas were dividedinto the following three regions, Region 1, Region 2, and Region 3 (FIG.21), and the division of these three regions was the same to thedivision of the three groups of the mean cell lengths of these hMSCs inthe above, i.e., the corresponding groupings of the ball diameters werethe same. Region 1 includes the four mean cell spread areas of the hMSCson the balls with diameters of 500 μm, 750 μm, 900 μm, and 1.1 mm, andthese four mean cell spread areas were fitted by a linear relation,y_(linear)=0.715x+1933.2. Region 2 includes the three mean cell spreadareas of the hMSCs on the balls with diameters of 2 mm, 3 mm, and 4 mm,and these three mean cell spread areas were fitted by another linearrelation y_(linear)=0.717x+4217.4. Note that the slope of Region 2'sfitting linear relation was very similar to that of Region 1's fittinglinear relation. Region 3 includes only the mean cell spread area of thehMSCs on the flat plates. The mean cell spread areas of the hMSCs on the4 mm- and 2 mm-balls was 56.5% and 45.1% of that of the hMSCs on theflat plates, respectively, whereas the mean cell spread area of theNIH-3T3 fibroblasts on the 2 mm-balls was 86.0% of that of thefibroblasts on the flat plates (Lee and Yang, 2012). This observationindicates that the cell spread areas of the hMSCs were also much moresensitive than those of the fibroblasts to the small curvatures or thelarge radii of the large substrate glass balls, e.g., the radii of 2 mmand 1 mm used here. This is consistent with the above observations onthe dependence of the hMSC morphology (FIG. 19) on substrate curvature,and on the dependences of the hMSC length and width (FIG. 20) onsubstrate curvature. Also, note that, from the 1.1 mm-balls to the 2mm-balls, there was a 149.7% abrupt rise in the mean cell spread area ofthe hMSCs.

DISCUSSION

The curvature of the surface to which a cell adheres has profoundeffects on cell attachment, migration, differentiation (with regard tostem cells) and morphology. The observed cell spreading anddifferentiation responses to substrate curvatures create newdirections/paradigms of research in the area of cell and tissuemechanobiology.

NIH-3T3 fibroblasts were cultured on the micro glass ball embedded PAgels with Young's moduli of 75 kPa, 10 kPa, and 1 kPa, respectively, andhave showed that some cells could wrap over the balls and these cellsnaturally isotropically spread over the balls and the adjacent gelsurfaces. The observations shown herein indicate that wrapping over aball is a method to realize cell natural isotropic-spreading where theresulting cell outline or boundary is roughly circular and smooth whichmeans the extent of the cell spreading in every direction is roughly thesame from the geometric center of the cell. For a fibroblast wrappedover a ball, the inventors have reasonably estimated the spread area onthe ball, the spread area on the gel surface, and the total spread areaof this cell. Based on the measured projected area of this cell, theinventor estimated the diameter of this cell and compared this estimatedvalue with the diameter of the micro glass ball to show the furtherspreading of this cell on the gel surface in the radial direction.Qualitative comparisons between the different fibroblasts, growing onthe micro glass balls with different diameters and embedded in PA gelswith different Young's moduli, for the above estimation results agreedwell with the theoretical reasonings.

The cell natural isotropic-spreading observed herein shows a newparadigm for controlling the spreading of a cell and its applications in3-D cellular bioengineering and mechanobiology. In the future, incombination with other imaging techniques, 3-D configurations of theembedded micro glass balls and the cells wrapping over the micro glassballs will be revealed. Micro glass ball embedded gels with controlledpositions of the embedded balls and controlled emerging-out heights ofthese balls from the gel surfaces will be developed to systematicallystudy the phenomena and the underlying mechanisms of the cell naturalisotropic-spreading and to explore the wide applications of the observedcell natural isotropic-spreading in cellular bioengineering andmechanobiology.

The dimensions and spread areas of NIH-3T3 fibroblasts and hMSCs platedon the micro glass balls with diameters from 5 μm to 4 mm were observedand measured. The results of these two cell types were compared. For theconvenience of the comparisons, FIG. 22 shows the measured results ofboth the fibroblasts and the hMSCs together as single plots for the celllengths (FIG. 22 (a)), cell widths (FIG. 22 (b)), cell aspect ratios(FIG. 22 (c)), and cell spread areas (FIG. 22 (d)), respectively, i.e.,FIG. 22 is the combination of FIG. 17 and FIG. 18, and FIG. 20 and FIG.21. The similarity between the responses of these two cell types to thesubstrate curvatures or the substrate ball diameters showed thefollowing: the mean cell spread areas of both cell types on the glassballs decreased with the decrease of the ball diameter.

The differences between the responses of these two cell types to thesubstrate curvatures or the substrate ball diameters included thefollowing conclusions of the comparisons between their responses. Amongthe used diameters of glass balls, the minimum diameter of a ball onwhich an hMSC can attach and spread was 500 μm, whereas the minimumdiameter of a ball on which an NIH-3T3 fibroblast can attach and spreadwithout wrapping over the ball was 58 μm (A fibroblast wrapping over aball means this fibroblast covered the entire upper exposed portion ofthe embedded ball in a PA gel and further spread on the adjacent gelsurface) (Lee and Yang, 2012). This finding shows that the attachmentsof the hMSCs were much more sensitive to the large curvatures or thesmall radii of the small substrate glass balls than those of thefibroblasts.

Below 500 μm, the next ball diameter that we used in the Examplespresented was 300 μm, and as stated in the Experiments above, no hMSCsattached and spread on the balls with diameters of 300 μm and below.From Table 3, the mean cell length of the hMSCs on the flat plates was408.4 μm. The spreading morphologies were observed and the dimensionsand spread areas were measured for hMSCs plated on the glass balls withdiameters from 500 μm to 4 mm and on the flat glass plates. While thespreading morphologies of the fibroblasts on the 2 mm-balls were almostindistinguishable from those of the fibroblasts on the flat plates, thehMSCs here on the 4 mm-balls were majorly spindle-shaped with only twolamellipodia, but the hMSCs on the flat plates were well-spread withrandomly-multiple lamellipodia. With the consideration that the surfaceof a 4 mm-ball is virtually flat with respect to the size of an hMSC,this finding indicates that the spreading morphologies of the hMSCs weremuch more sensitive to the small curvatures or the large radii of thelarge substrate glass balls than those of the fibroblasts. Putting thistogether with the relevant observations on the cell lengths, widths, andspread areas, described in the Examples herein, we say that thespreading morphologies, lengths, widths, and spread areas of the hMSCswere all much more sensitive to the small curvatures than those of thefibroblasts.

On the balls with diameters from 500 μm to 2 mm, the morphologies of thefibroblasts varied from the well-spread shapes on the 2 mm-balls to theround-shapes on the 500 μm-balls (Lee and Yang, 2012), whereas themorphologies of the hMSCs here on the balls with diameters from 500 μmto 4 mm were always majorly spindle-shaped with only two lamellipodia.This finding shows that the spreading morphologies of the fibroblastswere much more sensitive to the intermediate curvatures or the radii ofthe intermediate-sized substrate glass balls than those of the hMSCs.

Overall, starting from the case of the flat plates, the mean cell lengthof the hMSCs decreased monotonically with the decrease of the substrateball diameter. The values of the mean cell lengths of the hMSCs weredivided into the three groups, and the corresponding grouping of theball diameters was same to that for the mean cell spread areas of thesehMSCs, which may be understood by the observed similar mean cell widthsof the hMSCs on the balls with different diameters. The mean±SD resultsof all the cell lengths, all the cell widths, and all the cell aspectratios of the hMSCs on the balls with diameters of 500 μm and above,including the case of the flat plates, were 247.3±90.5 μm, 18.8±7.2 μm,and 0.091±0.049, respectively.

To study the underlying biophysical mechanisms for the observed effectsof the substrate curvatures on the spreading of the hMSCs, how theobserved spreading morphologies (FIG. 19) and measured sizes (FIGS. 20and 21) of the hMSCs can be scaled with the diameters of the substrateball was also investigated. In conclusion, the hMSCs have been culturedon the micro glass ball embedded PA gels, prepared with an improvedprotocol, and the glass balls had diameters from 5 μm to 4 mm. Thespreading morphologies of the hMSCs growing on the balls were observed,and it was found that the hMSCs on the balls were almost uniformlyspindle-shaped with two lamellipodia. The cell dimensions and spreadareas of these hMSCs were also measured, and the mean cell spread areashowed a decreasing tendency with the decreasing of the substrate balldiameter. The obtained results here for the hMSCs were compared withthose for the NIH-3T3 fibroblasts. The attachments of the hMSCs weremuch more sensitive to the large curvatures of the small balls thanthose of the fibroblasts. The spreading morphologies of the hMSCs weremuch more sensitive to the small curvatures of the large balls thanthose of the fibroblasts. But the spreading morphologies of thefibroblasts were much more sensitive to the intermediate curvatures ofthe intermediate-sized balls than those of the hMSCs. Therefore,substrate curvature directs cell attachment and spreading, and a largersubstrate curvature means less cell attachment and spreading, and asmaller substrate curvature means more cell attachment and spreading.This substrate curvature effect is different for different cell types.All these show that the curvature of a substrate is an importantgeometric parameter that can be utilized and tuned for cell and tissueengineering, and the idea of the micro glass ball embedded gels usedhere provides a paradigm for this purpose. Thus, substrate curvaturesaffect cell behaviors/functions, including cell adhesion, spreading,migration, division, differentiation, apoptosis, signal transduction,communication, etc.

All patents, patent applications, provisional applications, andpublications referred to or cited herein are incorporated by referencein their entirety, including all figures and tables, to the extent theyare not inconsistent with the explicit teachings of this specification.By citation of various references in this document, the Applicant doesnot admit any particular reference is “prior art” to their invention.

It should be understood that the examples and embodiments describedherein are for illustrative purposes only and that various modificationsor changes in light thereof will be suggested to persons skilled in theart and are to be included within the spirit and purview of thisapplication and the scope of the appended claims. In addition, anyelements or limitations of any invention or embodiment thereof disclosedherein can be combined with any and/or all other elements or limitations(individually or in any combination) or any other invention orembodiment thereof disclosed herein, and all such combinations arecontemplated with the scope of the disclosure without limitationthereto.

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What is claimed is:
 1. A method for guided induction of stem celldifferentiation, comprising: culturing a stem cell on a curved substratein the presence of cell culture media.
 2. The method of claim 1, whereinthe curved substrate comprises a coating selected from the groupconsisting of a cell adhesive, a cell adhesion-promotor, a cellrepellent, or a combination thereof.
 3. The method of claim 1, whereinthe curved substrate is selected from the group consisting of a convexsubstrate, a concave substrate, a spherical substrate, an ovalsubstrate, an elliptical substrate, and combinations thereof.
 4. Themethod of claim 1, wherein the curved substrate is a sphericalsubstrate.
 5. The method of claim 4, wherein the spherical substratecomprises a diameter of between about 500 μm and about 4 mm.
 6. Themethod of claim 4, wherein the spherical substrate comprises a diameterof between about 500 μm and about 2 mm.
 7. The method of claim 4,wherein the spherical substrate comprises a diameter of between about 4mm and about 6 mm.
 8. The method of claim 4, wherein the sphericalsubstrate comprises a diameter of between about 500 μm and about 6 mm.9. The method of claim 1, wherein the stem cell is a mesenchymal stemcell.
 10. The method of claim 9, wherein the cell culture mediacomprises osteocyte differentiation induction media, whereby the stemcell differentiates into an osteocyte.
 11. The method of claim 9,wherein the stem cell differentiates into an adipocyte.
 12. A kit forguided induction of stem cell differentiation, comprising: a firstreagent, wherein the first reagent comprises a curved substrate.
 13. Thekit of claim 12, wherein the curved substrate is selected from the groupconsisting of a convex substrate, a concave substrate, a sphericalsubstrate, an oval substrate, an elliptical substrate, and combinationsthereof.
 14. The kit of claim 12, wherein the curved substrate comprisesa coating selected from the group consisting of a cell adhesive, a celladhesion-promotor, a cell repellent, or a combination thereof.
 15. Thekit of claim 12, wherein the curved substrate is a spherical substrate.16. The kit of claim 15, wherein the spherical substrate comprises adiameter of between about 500 μm and about 6 mm.
 17. The kit of claim12, wherein first reagent is immobilized on a solid support.
 18. The kitof claim 15, wherein the spherical substrate comprises a diameter ofbetween about 500 μm and about 2 mm.
 19. The kit of claim 15, whereinthe spherical substrate comprises a diameter of between about 2 mm andabout 4 mm.
 20. The kit of claim 15, wherein the spherical substratecomprises a diameter of between about 4 mm and about 6 mm.